Sample records for gauss hypergeometric function

  1. Plasma Dispersion Function for the Kappa Distribution

    NASA Technical Reports Server (NTRS)

    Podesta, John J.

    2004-01-01

    The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

  2. A massive Feynman integral and some reduction relations for Appell functions

    NASA Astrophysics Data System (ADS)

    Shpot, M. A.

    2007-12-01

    New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

  3. Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl Teller Ginocchio potential wave functions

    NASA Astrophysics Data System (ADS)

    Michel, N.; Stoitsov, M. V.

    2008-04-01

    The fast computation of the Gauss hypergeometric function F12 with all its parameters complex is a difficult task. Although the F12 function verifies numerous analytical properties involving power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of z=e, are inaccessible using F12 power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the F12 function with real parameters. As in real case transformation theory, the large canceling terms occurring in F12 analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when |a|, |b|, |c| are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential involving F12 evaluations is considered. Program summaryProgram title: hyp_2F1, PTG_wf Catalogue identifier: AEAE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6839 No. of bytes in distributed program, including test data, etc.: 63 334 Distribution format: tar.gz Programming language: C++, Fortran 90 Computer: Intel i686 Operating system: Linux, Windows Word size: 64 bits Classification: 4.7 Nature of problem: The Gauss hypergeometric function F12, with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential is treated as a physical application. Solution method: The Gauss hypergeometric function F12 verifies linear transformation formulas allowing consideration of arguments of a small modulus which then can be handled by a power series. They, however, give rise to indeterminate or numerically unstable cases, when b-a and c-a-b are equal or close to integers. They are properly dealt with through analytical manipulations of the Lanczos expression providing the Gamma function. The remaining zones of the complex plane uncovered by transformation formulas are dealt with Taylor expansions of the F12 function around complex points where linear transformations can be employed. The Pöschl-Teller-Ginocchio potential wave functions are calculated directly with F12 evaluations. Restrictions: The algorithm provides full numerical precision in almost all cases for |a|, |b|, and |c| of the order of one or smaller, but starts to be less precise or unstable when they increase, especially through a, b, and c imaginary parts. While it is possible to run the code for moderate or large |a|, |b|, and |c| and obtain satisfactory results for some specified values, the code is very likely to be unstable in this regime. Unusual features: Two different codes, one for the hypergeometric function and one for the Pöschl-Teller-Ginocchio potential wave functions, are provided in C++ and Fortran 90 versions. Running time: 20,000 F12 function evaluations take an average of one second.

  4. Spiral Galaxy Lensing: A Model with Twist

    NASA Astrophysics Data System (ADS)

    Bell, Steven R.; Ernst, Brett; Fancher, Sean; Keeton, Charles R.; Komanduru, Abi; Lundberg, Erik

    2014-12-01

    We propose a single galaxy gravitational lensing model with a mass density that has a spiral structure. Namely, we extend the arcsine gravitational lens (a truncated singular isothermal elliptical model), adding an additional parameter that controls the amount of spiraling in the structure of the mass density. An important feature of our model is that, even though the mass density is sophisticated, we succeed in integrating the deflection term in closed form using a Gauss hypergeometric function. When the spiraling parameter is set to zero, this reduces to the arcsine lens.

  5. Higher-order automatic differentiation of mathematical functions

    NASA Astrophysics Data System (ADS)

    Charpentier, Isabelle; Dal Cappello, Claude

    2015-04-01

    Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

  6. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

    PubMed

    Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

    2015-10-02

    The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

  7. Inequalities of extended beta and extended hypergeometric functions.

    PubMed

    Mondal, Saiful R

    2017-01-01

    We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived.

  8. Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

    NASA Astrophysics Data System (ADS)

    Sanders, Sören; Holthaus, Martin

    2017-11-01

    We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

  9. RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

    DTIC Science & Technology

    Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

  10. f1: a code to compute Appell's F1 hypergeometric function

    NASA Astrophysics Data System (ADS)

    Colavecchia, F. D.; Gasaneo, G.

    2004-02-01

    In this work we present the FORTRAN code to compute the hypergeometric function F1( α, β1, β2, γ, x, y) of Appell. The program can compute the F1 function for real values of the variables { x, y}, and complex values of the parameters { α, β1, β2, γ}. The code uses different strategies to calculate the function according to the ideas outlined in [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29]. Program summaryTitle of the program: f1 Catalogue identifier: ADSJ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSJ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers: PC compatibles, SGI Origin2∗ Operating system under which the program has been tested: Linux, IRIX Programming language used: Fortran 90 Memory required to execute with typical data: 4 kbytes No. of bits in a word: 32 No. of bytes in distributed program, including test data, etc.: 52 325 Distribution format: tar gzip file External subprograms used: Numerical Recipes hypgeo [W.H. Press et al., Numerical Recipes in Fortran 77, Cambridge Univ. Press, 1996] or chyp routine of R.C. Forrey [J. Comput. Phys. 137 (1997) 79], rkf45 [L.F. Shampine and H.H. Watts, Rep. SAND76-0585, 1976]. Keywords: Numerical methods, special functions, hypergeometric functions, Appell functions, Gauss function Nature of the physical problem: Computing the Appell F1 function is relevant in atomic collisions and elementary particle physics. It is usually the result of multidimensional integrals involving Coulomb continuum states. Method of solution: The F1 function has a convergent-series definition for | x|<1 and | y|<1, and several analytic continuations for other regions of the variable space. The code tests the values of the variables and selects one of the precedent cases. In the convergence region the program uses the series definition near the origin of coordinates, and a numerical integration of the third-order differential parametric equation for the F1 function. Also detects several special cases according to the values of the parameters. Restrictions on the complexity of the problem: The code is restricted to real values of the variables { x, y}. Also, there are some parameter domains that are not covered. These usually imply differences between integer parameters that lead to negative integer arguments of Gamma functions. Typical running time: Depends basically on the variables. The computation of Table 4 of [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29] (64 functions) requires approximately 0.33 s in a Athlon 900 MHz processor.

  11. Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Neretin, Yu A

    2006-12-31

    A family of non-complete orthogonal systems of functions on the ray [0,{infinity}] depending on three real parameters {alpha}, {beta}, {theta} is constructed. The elements of this system are piecewise hypergeometric functions with singularity at x=1. For {theta}=0 these functions vanish on [1,{infinity}) and the system is reduced to the Jacobi polynomials P{sub n}{sup {alpha}}{sup ,{beta}} on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P{sub n+{theta}}{sup {alpha}}{sup ,{beta}}. They are eigenfunctions of an exotic Sturm-Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem ismore » found.« less

  12. Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

    NASA Astrophysics Data System (ADS)

    Abdelaziz, Y.; Maillard, J.-M.

    2017-05-01

    We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to develop more differentially algebraic symmetry analysis in physics.

  13. A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

    DTIC Science & Technology

    1978-03-01

    Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

  14. HYPERDIRE-HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function FC of three variables

    NASA Astrophysics Data System (ADS)

    Bytev, Vladimir V.; Kniehl, Bernd A.

    2016-09-01

    We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function FC of three variables. Catalogue identifier: AEPP_v4_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPP_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 243461 No. of bytes in distributed program, including test data, etc.: 61610782 Distribution format: tar.gz Programming language: Mathematica. Computer: All computers running Mathematica. Operating system: Operating systems running Mathematica. Classification: 4.4. Does the new version supersede the previous version?: No, it significantly extends the previous version. Nature of problem: Reduction of hypergeometric function FC of three variables to a set of basis functions. Solution method: Differential reduction. Reasons for new version: The extension package allows the user to handle the Lauricella function FC of three variables. Summary of revisions: The previous version goes unchanged. Running time: Depends on the complexity of the problem.

  15. Tree-level gluon amplitudes on the celestial sphere

    NASA Astrophysics Data System (ADS)

    Schreiber, Anders Ø.; Volovich, Anastasia; Zlotnikov, Michael

    2018-06-01

    Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary n-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian Gr (4 , n), while generic non-MHV amplitudes are given by more complicated Gelfand A-hypergeometric functions.

  16. A Unified Approach to Electromagnetic Wave Propagation in Turbulence and the Evaluation of Multiparameter Integrals

    DTIC Science & Technology

    1988-07-01

    The solutions in some cases have been made more general , as in the papers of Fried2 and Tyler3 by defining normnalized quantities; the tabular and... generalized hypergeometric functions. For that case, he shows that the integral, which can be transformed into a Mellin- Barnes integral, can be expressed as a...finite sum of generalized hypergeometric functions which are equivalent to a Meijer’s G-function. He briefly considers the case in which the

  17. Derivatives of Horn hypergeometric functions with respect to their parameters

    NASA Astrophysics Data System (ADS)

    Ancarani, L. U.; Del Punta, J. A.; Gasaneo, G.

    2017-07-01

    The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn's functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.

  18. Hypergeometric type operators and their supersymmetric partners

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cotfas, Nicolae; Cotfas, Liviu Adrian

    2011-05-15

    The generalization of the factorization method performed by Mielnik [J. Math. Phys. 25, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to hypergeometric type operators. It is based on some solvable Riccati equations and leads to a unitary description of the quantum systems exactly solvable in terms of orthogonal polynomials or associated special functions.

  19. Laplace approximation for Bessel functions of matrix argument

    NASA Astrophysics Data System (ADS)

    Butler, Ronald W.; Wood, Andrew T. A.

    2003-06-01

    We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

  20. Complete N-point superstring disk amplitude II. Amplitude and hypergeometric function structure

    NASA Astrophysics Data System (ADS)

    Mafra, Carlos R.; Schlotterer, Oliver; Stieberger, Stephan

    2013-08-01

    Using the pure spinor formalism in part I (Mafra et al., preprint [1]) we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed by a sum over (N-3)! Yang-Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space-time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Gröbner basis analysis provides independent sets of rational functions in the Euler integrals. In contrast to [1] here we use momenta redefined by a factor of i. As a consequence the signs of the kinematic invariants are flipped, e.g. |→|.

  1. On the performance of dual-hop mixed RF/FSO wireless communication system in urban area over aggregated exponentiated Weibull fading channels with pointing errors

    NASA Astrophysics Data System (ADS)

    Wang, Yue; Wang, Ping; Liu, Xiaoxia; Cao, Tian

    2018-03-01

    The performance of decode-and-forward dual-hop mixed radio frequency / free-space optical system in urban area is studied. The RF link is modeled by the Nakagami-m distribution and the FSO link is described by the composite exponentiated Weibull (EW) fading channels with nonzero boresight pointing errors (NBPE). For comparison, the ABER results without pointing errors (PE) and those with zero boresight pointing errors (ZBPE) are also provided. The closed-form expression for the average bit error rate (ABER) in RF link is derived with the help of hypergeometric function, and that in FSO link is obtained by Meijer's G and generalized Gauss-Laguerre quadrature functions. Then, the end-to-end ABERs with binary phase shift keying modulation are achieved on the basis of the computed ABER results of RF and FSO links. The end-to-end ABER performance is further analyzed with different Nakagami-m parameters, turbulence strengths, receiver aperture sizes and boresight displacements. The result shows that with ZBPE and NBPE considered, FSO link suffers a severe ABER degradation and becomes the dominant limitation of the mixed RF/FSO system in urban area. However, aperture averaging can bring significant ABER improvement of this system. Monte Carlo simulation is provided to confirm the validity of the analytical ABER expressions.

  2. A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

    PubMed

    Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

    2013-01-01

    As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

  3. Further summation formulae related to generalized harmonic numbers

    NASA Astrophysics Data System (ADS)

    Zheng, De-Yin

    2007-11-01

    By employing the univariate series expansion of classical hypergeometric series formulae, Shen [L.-C. Shen, Remarks on some integrals and series involving the Stirling numbers and [zeta](n), Trans. Amer. Math. Soc. 347 (1995) 1391-1399] and Choi and Srivastava [J. Choi, H.M. Srivastava, Certain classes of infinite series, Monatsh. Math. 127 (1999) 15-25; J. Choi, H.M. Srivastava, Explicit evaluation of Euler and related sums, Ramanujan J. 10 (2005) 51-70] investigated the evaluation of infinite series related to generalized harmonic numbers. More summation formulae have systematically been derived by Chu [W. Chu, Hypergeometric series and the Riemann Zeta function, Acta Arith. 82 (1997) 103-118], who developed fully this approach to the multivariate case. The present paper will explore the hypergeometric series method further and establish numerous summation formulae expressing infinite series related to generalized harmonic numbers in terms of the Riemann Zeta function [zeta](m) with m=5,6,7, including several known ones as examples.

  4. Comment on “Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term” [J. Math. Phys. 51, 023525 (2010)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ghoumaid, A.; Benamira, F.; Guechi, L.

    2016-02-15

    It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given is incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions {sub 2}F{sub 1}(a, b, c; z). The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.

  5. Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Allen, G.

    1972-01-01

    The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.

  6. Reliability estimation of a N- M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution

    NASA Astrophysics Data System (ADS)

    Liu, Yiming; Shi, Yimin; Bai, Xuchao; Zhan, Pei

    2018-01-01

    In this paper, we study the estimation for the reliability of a multicomponent system, named N- M-cold-standby redundancy system, based on progressive Type-II censoring sample. In the system, there are N subsystems consisting of M statistically independent distributed strength components, and only one of these subsystems works under the impact of stresses at a time and the others remain as standbys. Whenever the working subsystem fails, one from the standbys takes its place. The system fails when the entire subsystems fail. It is supposed that the underlying distributions of random strength and stress both belong to the generalized half-logistic distribution with different shape parameter. The reliability of the system is estimated by using both classical and Bayesian statistical inference. Uniformly minimum variance unbiased estimator and maximum likelihood estimator for the reliability of the system are derived. Under squared error loss function, the exact expression of the Bayes estimator for the reliability of the system is developed by using the Gauss hypergeometric function. The asymptotic confidence interval and corresponding coverage probabilities are derived based on both the Fisher and the observed information matrices. The approximate highest probability density credible interval is constructed by using Monte Carlo method. Monte Carlo simulations are performed to compare the performances of the proposed reliability estimators. A real data set is also analyzed for an illustration of the findings.

  7. Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

    NASA Astrophysics Data System (ADS)

    Conway, John T.; Cohl, Howard S.

    2010-06-01

    A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

  8. Special solutions to Chazy equation

    NASA Astrophysics Data System (ADS)

    Varin, V. P.

    2017-02-01

    We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

  9. Solution of fractional kinetic equation by a class of integral transform of pathway type

    NASA Astrophysics Data System (ADS)

    Kumar, Dilip

    2013-04-01

    Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

  10. HYPERSAMP - HYPERGEOMETRIC ATTRIBUTE SAMPLING SYSTEM BASED ON RISK AND FRACTION DEFECTIVE

    NASA Technical Reports Server (NTRS)

    De, Salvo L. J.

    1994-01-01

    HYPERSAMP is a demonstration of an attribute sampling system developed to determine the minimum sample size required for any preselected value for consumer's risk and fraction of nonconforming. This statistical method can be used in place of MIL-STD-105E sampling plans when a minimum sample size is desirable, such as when tests are destructive or expensive. HYPERSAMP utilizes the Hypergeometric Distribution and can be used for any fraction nonconforming. The program employs an iterative technique that circumvents the obstacle presented by the factorial of a non-whole number. HYPERSAMP provides the required Hypergeometric sample size for any equivalent real number of nonconformances in the lot or batch under evaluation. Many currently used sampling systems, such as the MIL-STD-105E, utilize the Binomial or the Poisson equations as an estimate of the Hypergeometric when performing inspection by attributes. However, this is primarily because of the difficulty in calculation of the factorials required by the Hypergeometric. Sampling plans based on the Binomial or Poisson equations will result in the maximum sample size possible with the Hypergeometric. The difference in the sample sizes between the Poisson or Binomial and the Hypergeometric can be significant. For example, a lot size of 400 devices with an error rate of 1.0% and a confidence of 99% would require a sample size of 400 (all units would need to be inspected) for the Binomial sampling plan and only 273 for a Hypergeometric sampling plan. The Hypergeometric results in a savings of 127 units, a significant reduction in the required sample size. HYPERSAMP is a demonstration program and is limited to sampling plans with zero defectives in the sample (acceptance number of zero). Since it is only a demonstration program, the sample size determination is limited to sample sizes of 1500 or less. The Hypergeometric Attribute Sampling System demonstration code is a spreadsheet program written for IBM PC compatible computers running DOS and Lotus 1-2-3 or Quattro Pro. This program is distributed on a 5.25 inch 360K MS-DOS format diskette, and the program price includes documentation. This statistical method was developed in 1992.

  11. Cancellation of factorials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zudilin, W W

    2001-08-31

    An arithmetical property allowing an improvement of some number-theoretic estimates is studied. Previous results were mostly qualitative. Application of quantitative results of the paper to the class of generalized hypergeometric G-functions extends the set of irrational numbers representable as values of these functions.

  12. New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

    NASA Astrophysics Data System (ADS)

    Abd-Elhameed, W. M.

    2017-07-01

    In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

  13. Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose-Hubbard model

    NASA Astrophysics Data System (ADS)

    Sanders, Sören; Holthaus, Martin

    2017-10-01

    We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

  14. Completeness of the Coulomb Wave Functions in Quantum Mechanics

    ERIC Educational Resources Information Center

    Mukunda, N.

    1978-01-01

    Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

  15. Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Middleton, Chad A.; Stanley, Ethan

    2011-10-15

    We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

  16. Evaluating Feynman integrals by the hypergeometry

    NASA Astrophysics Data System (ADS)

    Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

    2018-02-01

    The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

  17. A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

    NASA Astrophysics Data System (ADS)

    Ishkhanyan, Tigran A.; Krainov, Vladimir P.; Ishkhanyan, Artur M.

    2018-05-01

    We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term x-1/2 with arbitrary strength and a repulsive centrifugal barrier core x-2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

  18. Dirac-Kähler particle in Riemann spherical space: boson interpretation

    NASA Astrophysics Data System (ADS)

    Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

    2015-11-01

    In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.

  19. Photon-number-resolving detectors and their role in quantifying quantum correlations

    NASA Astrophysics Data System (ADS)

    Tan, Si-Hui; Krivitsky, Leonid A.; Englert, Berthold-Georg

    2016-09-01

    Harnessing entanglement as a resource is the main workhorse of many quantum protocols, and establishing the degree of quantum correlations of quantum states is an important certification process that has to take place prior to any implementations of these quantum protocols. The emergence of photodetectors known as photon-number-resolving detectors (PNRDs) that allow for accounting of photon numbers simultaneously arriving at the detectors has led to the need for modeling accurately and applying them for use in the certification process. Here we study the variance of difference of photocounts (VDP) of two PNRDs, which is one measure of quantum correlations, under the effects of loss and saturation. We found that it would be possible to distinguish between the classical correlation of a two-mode coherent state and the quantum correlation of a twin-beam state within some photo count regime of the detector. We compare the behavior of two such PNRDs. The first for which the photocount statistics follow a binomial distribution accounting for losses, and the second is that of Agarwal, Vogel, and Sperling for which the incident beam is first split and then separately measured by ON/OFF detectors. In our calculations, analytical expressions are derived for the variance of difference where possible. In these cases, Gauss' hypergeometric function appears regularly, giving an insight to the type of quantum statistics the photon counting gives in these PNRDs. The different mechanisms of the two types of PNRDs leads to quantitative differences in their VDP.

  20. Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

    NASA Astrophysics Data System (ADS)

    Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

    2017-03-01

    Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

  1. QCD triple Pomeron coupling from string amplitudes

    NASA Astrophysics Data System (ADS)

    Bialas, A.; Navelet, H.; Peschanski, R.

    1998-06-01

    Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

  2. Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

    DTIC Science & Technology

    2014-04-01

    The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

  3. Numerical Grid Generation and Potential Airfoil Analysis and Design

    DTIC Science & Technology

    1988-01-01

    Gauss- Seidel , SOR and ADI iterative methods e JACOBI METHOD In the Jacobi method each new value of a function is computed entirely from old values...preceding iteration and adding the inhomogeneous (boundary condition) term. * GAUSS- SEIDEL METHOD When we compute I in a Jacobi method, we have already...Gauss- Seidel method. Sufficient condition for p convergence of the Gauss- Seidel method is diagonal-dominance of [A].9W e SUCESSIVE OVER-RELAXATION (SOR

  4. Magnetic expansion of Nekrasov theory: The SU(2) pure gauge theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    He Wei; Miao Yangang

    It is recently claimed by Nekrasov and Shatashvili that the N=2 gauge theories in the {Omega} background with {epsilon}{sub 1}=({h_bar}/2{pi}), {epsilon}{sub 2}=0 are related to the quantization of certain algebraic integrable systems. We study the special case of SU(2) pure gauge theory; the corresponding integrable model is the A{sub 1} Toda model, which reduces to the sine-Gordon quantum mechanics problem. The quantum effects can be expressed as the WKB series written analytically in terms of hypergeometric functions. We obtain the magnetic and dyonic expansions of the Nekrasov theory by studying the property of hypergeometric functions in the magnetic and dyonicmore » regions on the moduli space. We also discuss the relation between the electric-magnetic duality of gauge theory and the action-action duality of the integrable system.« less

  5. Average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence

    NASA Astrophysics Data System (ADS)

    Liu, Dajun; Wang, Guiqiu; Wang, Yaochuan

    2018-01-01

    Based on the Huygens-Fresnel integral and the relationship of Lorentz distribution and Hermite-Gauss function, the average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence have been investigated by using numerical examples. The influences of beam parameters and oceanic turbulence on the propagation properties are also discussed in details. It is shown that the partially coherent Lorentz-Gauss beam with smaller coherence length will spread faster in oceanic turbulence, and the stronger oceanic turbulence will accelerate the spreading of partially coherent Lorentz-Gauss beam in oceanic turbulence.

  6. Evaluation of Fuel Cell Operation and Degradation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Williams, Mark; Gemmen, Randall; Richards, George

    The concepts of area specific resistance (ASR) and degradation are developed for different fuel cell operating modes. The concepts of exergetic efficiency and entropy production were applied to ASR and degradation. It is shown that exergetic efficiency is a time-dependent function useful describing the thermal efficiency of a fuel cell and the change in thermal efficiency of a degrading fuel cell. Entropy production was evaluated for the cases of constant voltage operation and constant current operation of the fuel cell for a fuel cell undergoing ohmic degradation. It was discovered that the Gaussian hypergeometric function describes the cumulative entropy andmore » electrical work produced by fuel cells operating at constant voltage. The Gaussian hypergeometric function is found in many applications in modern physics. This paper builds from and is an extension of several papers recently published by the authors in the Journal of The Electrochemical Society (ECS), ECS Transactions, Journal of Power Sources, and the Journal of Fuel Cell Science and Technology.« less

  7. On mini-superspace limit of boundary three-point function in Liouville field theory

    NASA Astrophysics Data System (ADS)

    Apresyan, Elena; Sarkissian, Gor

    2017-12-01

    We study the mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.

  8. Generalized spheroidal wave equation and limiting cases

    NASA Astrophysics Data System (ADS)

    Figueiredo, B. D. Bonorino

    2007-01-01

    We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

  9. Comparisons between real and complex Gauss wavelet transform methods of three-dimensional shape reconstruction

    NASA Astrophysics Data System (ADS)

    Xu, Luopeng; Dan, Youquan; Wang, Qingyuan

    2015-10-01

    The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.

  10. Some Families of the Incomplete H-Functions and the Incomplete \\overline H -Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications

    NASA Astrophysics Data System (ADS)

    Srivastava, H. M.; Saxena, R. K.; Parmar, R. K.

    2018-01-01

    Our present investigation is inspired by the recent interesting extensions (by Srivastava et al. [35]) of a pair of the Mellin-Barnes type contour integral representations of their incomplete generalized hypergeometric functions p γ q and p Γ q by means of the incomplete gamma functions γ( s, x) and Γ( s, x). Here, in this sequel, we introduce a family of the relatively more general incomplete H-functions γ p,q m,n ( z) and Γ p,q m,n ( z) as well as their such special cases as the incomplete Fox-Wright generalized hypergeometric functions p Ψ q (γ) [ z] and p Ψ q (Γ) [ z]. The main object of this paper is to study and investigate several interesting properties of these incomplete H-functions, including (for example) decomposition and reduction formulas, derivative formulas, various integral transforms, computational representations, and so on. We apply some substantially general Riemann-Liouville and Weyl type fractional integral operators to each of these incomplete H-functions. We indicate the easilyderivable extensions of the results presented here that hold for the corresponding incomplete \\overline H -functions as well. Potential applications of many of these incomplete special functions involving (for example) probability theory are also indicated.

  11. Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence.

    PubMed

    Liu, Dajun; Yin, Hongming; Wang, Guiqiu; Wang, Yaochuan

    2017-11-01

    The partially coherent Lorentz-Gauss vortex beam generated by a Schell-model source has been introduced. Based on the extended Huygens-Fresnel principle, the cross-spectral density function of a partially coherent Lorentz-Gauss vortex beam propagating in oceanic turbulence is derived. The influences of coherence length, topological charge M, and oceanic turbulence on the spreading properties and position of the coherence vortex for a partially coherent Lorentz-Gauss vortex beam are analyzed in detail. The results show that a partially coherent Lorentz-Gauss vortex beam propagating in stronger oceanic turbulence will evolve into a Gaussian-like beam more rapidly as the propagation distance increases, and the number of coherent vortices will change.

  12. Technique for evaluation of the strong potential Born approximation for electron capture

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sil, N.C.; McGuire, J.H.

    1985-04-01

    A technique is presented for evaluating differential cross sections in the strong potential Born (SPB) approximation. Our final expression is expressed as a finite sum of one-dimensional integrals, expressible as a finite sum of derivatives of hypergeometric functions.

  13. Crossing of the phantom divide using tachyon-Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sadeghi, J.; Banijamali, A.; Milani, F.

    2009-06-15

    In this paper we consider two models. First, we study tachyon-Gauss-Bonnet gravity and obtain the condition of the equation of state crossing -1. Second, we discuss the modified Gauss-Bonnet gravity with the tachyon field and show the condition of {omega} crossing -1. Also, we plot figures for {omega} numerically in special potential and coupling function.

  14. On the solving of one type of problems of mathematical physics

    NASA Astrophysics Data System (ADS)

    Chebakova, V. J.; Gerasimov, A. V.; Kirpichnikov, A. P.

    2016-11-01

    A relationship between generalized hypergeometric functions of a special type and modified Bessel functions has been established. Using this relationship the solution of inhomogeneous differential equations of Bessel type containing even degrees of an independent variable in the right-hand part can be expressed in a form convenient for engineering and technical applications.

  15. Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lahiri, Sayantani, E-mail: sayantani.lahiri@gmail.com

    2017-01-01

    In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by amore » non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.« less

  16. On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr; Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu

    In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case ofmore » a slightly more general potential than the one for harmonic oscillator.« less

  17. Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

    NASA Astrophysics Data System (ADS)

    Mingari Scarpello, Giovanni; Ritelli, Daniele

    2018-06-01

    The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

  18. Analytical solutions of the Klein-Gordon equation for Manning-Rosen potential with centrifugal term through Nikiforov-Uvarov method

    NASA Astrophysics Data System (ADS)

    Hatami, N.; Setare, M. R.

    2017-10-01

    We present approximate analytical solutions of the Klein-Gordon equation with arbitrary l state for the Manning-Rosen potential using the Nikiforov-Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

  19. Luigi Gatteschi's work on asymptotics of special functions and their zeros

    NASA Astrophysics Data System (ADS)

    Gautschi, Walter; Giordano, Carla

    2008-12-01

    A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

  20. Bounce universe from string-inspired Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bamba, Kazuharu; Makarenko, Andrey N.; Myagky, Alexandr N.

    2015-04-01

    We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is movedmore » to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.« less

  1. Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions

    NASA Astrophysics Data System (ADS)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.

    2004-03-01

    We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.

  2. Self-healing of Hermite-Gauss and Ince-Gauss beams

    NASA Astrophysics Data System (ADS)

    Aguirre-Olivas, Dilia; Mellado-Villaseñor, Gabriel; Arrizón, Victor; Chávez-Cerda, Sabino

    2015-08-01

    We analyze and demonstrate, numerically and experimentally, the self-healing effect in scaled propagation invariant beams, subject to opaque obstructions. The effect is quantitatively evaluated employing the Root Mean Square deviation and the similarity function.

  3. (q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

    2010-10-15

    From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

  4. Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions

    ERIC Educational Resources Information Center

    Wroughton, Jacqueline; Cole, Tarah

    2013-01-01

    Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…

  5. Computation of the Complex Probability Function

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Trainer, Amelia Jo; Ledwith, Patrick John

    The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n th degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

  6. Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

    The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

  7. Entangled singularity patterns of photons in Ince-Gauss modes

    NASA Astrophysics Data System (ADS)

    Krenn, Mario; Fickler, Robert; Huber, Marcus; Lapkiewicz, Radek; Plick, William; Ramelow, Sven; Zeilinger, Anton

    2013-01-01

    Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify two-dimensional and three-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we nonlocally steer the singularity structure of its entangled partner, while the initial singularity structure of the photons is undefined. In addition we measure an Ince-Gauss specific quantum-correlation function with possible use in future quantum communication protocols.

  8. A note on the bounds of the error of Gauss-Turan-type quadratures

    NASA Astrophysics Data System (ADS)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.

    2007-03-01

    This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.

  9. An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions. [radiative transfer

    NASA Technical Reports Server (NTRS)

    Fricke, C. L.

    1975-01-01

    A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

  10. Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

    NASA Astrophysics Data System (ADS)

    Bentalha, Zine el abidine

    2018-06-01

    Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

  11. Dissociative Electron Attachment to Rovibrationally Excited Molecules

    DTIC Science & Technology

    1987-08-31

    obtained in some recent papers.4’ - In Sec. IV of the present L,(0, (00 paper we will obtain some general recursion relations among where these matrix... general five-term From the generating function of Hermite polynomials , recursion relation (32) is obtained which is valid for the matrix elements of...for the generation of the functions for increasing 1. One convenient way to evaluate a Q, function is to write it in terms of Gaussian hypergeometric

  12. Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

    NASA Astrophysics Data System (ADS)

    Malik, Pradeep; Swaminathan, A.

    2010-11-01

    In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

  13. Hypergeometric Gaussian beam and its propagation in turbulence

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil Tanyer; Cai, Yangjian

    2012-10-01

    We study propagation characteristics of hypergeometric Gaussian beam in turbulence. In this context, we formulate the receiver plane intensity using extended Huygens-Fresnel integral. From the graphical results, it is seen that, after propagation, hypergeometric Gaussian will in general assume the shape of a dark hollow beam at topological charges other than zero. Increasing values of topological charge will make the beam broader with steeper walls. On the other hand, higher values of hollowness parameter will contract into a narrower shape. Raising the topological charge or the hollowness parameter individually will cause outer rings to appear. Both increased levels of turbulence and longer propagation distances will accelerate the beam evolution and help reach the final Gaussian shape sooner. At lower wavelengths, there will be less beam spreading.

  14. Bounds of the error of Gauss-Turan-type quadratures

    NASA Astrophysics Data System (ADS)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.

    2005-06-01

    We consider the remainder term of the Gauss-Turan quadrature formulaefor analytic functions in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses or circles. A strong error analysis is given for the case with a generalized class of weight functions, introduced recently by Gori and Micchelli. Also, we discuss a general case with an even weight function defined on [-1,1]. Numerical results are included.

  15. On Exact Solutions of Rarefaction-Rarefaction Interactions in Compressible Isentropic Flow

    NASA Astrophysics Data System (ADS)

    Jenssen, Helge Kristian

    2017-12-01

    Consider the interaction of two centered rarefaction waves in one-dimensional, compressible gas flow with pressure function p(ρ )=a^2ρ ^γ with γ >1. The classic hodograph approach of Riemann provides linear 2nd order equations for the time and space variables t, x as functions of the Riemann invariants r, s within the interaction region. It is well known that t( r, s) can be given explicitly in terms of the hypergeometric function. We present a direct calculation (based on works by Darboux and Martin) of this formula, and show how the same approach provides an explicit formula for x( r, s) in terms of Appell functions (two-variable hypergeometric functions). Motivated by the issue of vacuum and total variation estimates for 1-d Euler flows, we then use the explicit t-solution to monitor the density field and its spatial variation in interactions of two centered rarefaction waves. It is found that the variation is always non-monotone, and that there is an overall increase in density variation if and only if γ >3. We show that infinite duration of the interaction is characterized by approach toward vacuum in the interaction region, and that this occurs if and only if the Riemann problem defined by the extreme initial states generates a vacuum. Finally, it is verified that the minimal density in such interactions decays at rate O(1)/ t.

  16. Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

    DTIC Science & Technology

    2001-09-11

    Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

  17. Internal force field in proteins seen by divergence entropy

    PubMed Central

    Marchewka, Damian; Banach, Mateusz; Roterman, Irena

    2011-01-01

    The characteristic distribution of non-binding interactions in a protein is described. It establishes that hydrophobic interactions can be characterized by suitable 3D Gauss functions while electrostatic interactions generally follow a random distribution. The implementation of this observation suggests differentiated optimization procedure for these two types of interactions. The electrostatic interaction may follow traditional energy optimization while the criteria for convergence shall measure the accordance with 3-D Gauss function. PMID:21769190

  18. Production of confluent hypergeometric beam by computer-generated hologram

    NASA Astrophysics Data System (ADS)

    Chen, Jiannong; Wang, Gang; Xu, Qinfeng

    2011-02-01

    Because of their spiral wave front, phase singularity, zero-intensity center and orbital angular momentum, dark hollow vortex beams have been found many applications in the field of atom optics such as atom cooling, atom transport and atom guiding. In this paper, a method for generating confluent hypergeometric beam by computer-generated hologram displayed on the spatial light modulator is presented. The hologram is formed by interference between a single ring Laguerre-Gaussian beam and a plane wave. The far-field Fraunhofer diffraction of this optical field transmitted from the hologram is the confluent hypergeometric beam. This beam is a circular symmetric beam which has a phase singularity, spiral wave front, zero-intensity center, and intrinsic orbital angular momentum. It is a new dark hollow vortex beam.

  19. Stability of anti-de sitter space in Einstein-Gauss-Bonnet gravity.

    PubMed

    Deppe, Nils; Kolly, Allison; Frey, Andrew; Kunstatter, Gabor

    2015-02-20

    Recently it has been argued that in Einstein gravity anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass-energy content of the spacetime is too small, thereby restoring the stability of anti-de Sitter spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

  20. The Gauss-Bonnet operator of an infinite graph

    NASA Astrophysics Data System (ADS)

    Anné, Colette; Torki-Hamza, Nabila

    2015-06-01

    We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator , based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.

  1. Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

    DTIC Science & Technology

    2002-07-25

    Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

  2. Complex Analysis and Related Topics. Proceedings of the Conference held in Amsterdam on 27 - 29 January 1993

    DTIC Science & Technology

    1993-01-29

    Bessel functions and Jacobi functions (cf. [2]). References [1] R. Askey & J. Wilson, Some basic hypergeometric orthogonal polynomials that gen- eralize...1; 1] can be treated as a part of general theory of T-systems (see [81 for that theory and [7] for some aspects of the Chebyshev polynomials theory...waves in elastic media. It has been known for some time that these multiplicities sometimes occur for topological reasons and are present generically , see

  3. Orthogonal Polynomials Associated with Complementary Chain Sequences

    NASA Astrophysics Data System (ADS)

    Behera, Kiran Kumar; Sri Ranga, A.; Swaminathan, A.

    2016-07-01

    Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.

  4. Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces.

    PubMed

    Di Claudio, Elio D; Jacovitti, Giovanni; Laurenti, Alberto

    2010-05-01

    A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

  5. Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories

    NASA Astrophysics Data System (ADS)

    Antoniou, G.; Bakopoulos, A.; Kanti, P.

    2018-03-01

    We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f (ϕ ) . We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f (ϕ ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f (ϕ ).

  6. Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories.

    PubMed

    Antoniou, G; Bakopoulos, A; Kanti, P

    2018-03-30

    We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f(ϕ). We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f(ϕ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f(ϕ).

  7. Noether symmetries in Gauss-Bonnet-teleparallel cosmology.

    PubMed

    Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F

    2016-01-01

    A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.

  8. Elementary functions in thermodynamic Bethe ansatz

    NASA Astrophysics Data System (ADS)

    Suzuki, J.

    2015-05-01

    Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

  9. Umbral Calculus and Holonomic Modules in Positive Characteristic

    NASA Astrophysics Data System (ADS)

    Kochubei, Anatoly N.

    2006-03-01

    In the framework of analysis over local fields of positive characteristic, we develop algebraic tools for introducing and investigating various polynomial systems. In this survey paper we describe a function field version of umbral calculus developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. We consider modules over the Weyl-Carlitz ring, a function field counterpart of the Weyl algebra. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's hypergeometric polynomials, and analogs of binomial coefficients arising in the positive characteristic version of umbral calculus, generate holonomic modules.

  10. Fast summation of divergent series and resurgent transseries from Meijer-G approximants

    NASA Astrophysics Data System (ADS)

    Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.

    2018-05-01

    We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

  11. New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.

    PubMed

    Milne, S C

    1996-12-24

    In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi's (1829) 4 and 8 squares identities to 4n(2) or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan's tau function tau(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the eta-function identities in appendix I of Macdonald's work [Macdonald, I. G. (1972) Invent. Math. 15, 91-143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415-456] identities involving representing a positive integer by sums of 4n(2) or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson's C(l) nonterminating (6)phi(5) summation theorem, and Andrews' basic hypergeometric series proof of Jacobi's 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n(2) or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

  12. Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

    NASA Astrophysics Data System (ADS)

    Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

    2018-04-01

    Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

  13. Faà di Bruno's formula and the distributions of random partitions in population genetics and physics.

    PubMed

    Hoppe, Fred M

    2008-06-01

    We show that the formula of Faà di Bruno for the derivative of a composite function gives, in special cases, the sampling distributions in population genetics that are due to Ewens and to Pitman. The composite function is the same in each case. Other sampling distributions also arise in this way, such as those arising from Dirichlet, multivariate hypergeometric, and multinomial models, special cases of which correspond to Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann distributions in physics. Connections are made to compound sampling models.

  14. On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

    NASA Technical Reports Server (NTRS)

    Gottlieb, David; Shu, Chi-Wang

    1994-01-01

    The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

  15. Diffraction Theory for Polygonal Apertures

    DTIC Science & Technology

    1988-07-01

    and utilized oblate spheroidal vector wave functions, and Nomura and Katsura (1955), who employed an expansion of the hypergeometric polynomial ...21 2 - 1 4, 2 - 1 3 4k3 - 3k 8 3 - 4 factor relates directly to the orthogonality relations for the Chebyshev polynomials given below. I T(Q TieQdk...convergence. 3.1.2.2 Gaussian Illuminated Corner In the sample calculation just discussed we discovered some of the basic characteristics of the GBE

  16. Dynamic analysis of multirigid-body system based on the Gauss principle

    NASA Astrophysics Data System (ADS)

    Lilov, L.; Lorer, M.

    Two different approaches can be used for solving the basic dynamic problem in the case of a multirigid body system. The first approach is based on the derivation of the nonlinear equations of motion of the mechanical system, while the second approach is concerned with the direct derivation of the unknown accelerations. Using the Gauss principle, the accelerations can be determined by using the condition for the minimum of a functional. The present investigation is concerned with an algorithm for a dynamical study of a multibody system on the basis of the Gauss principle. The system may contain an arbitrary number of closed loops. The main purpose of the proposed algorithm is the investigation of the dynamics of industrial manipulators, robots, and similar mechanisms.

  17. Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories

    NASA Astrophysics Data System (ADS)

    Antoniou, G.; Bakopoulos, A.; Kanti, P.

    2018-04-01

    In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, which studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically flat black-hole solutions with nontrivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a nonmonotonic behavior, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area, and entropy of our solutions.

  18. Effect of Convection on Weld Pool Shape and Microstructure.

    DTIC Science & Technology

    1986-07-01

    latent heat of fusion 11 u dynamic viscosity Iwo V kinematic viscosity P density a Stefan -Boltzman constant stress tensor 0, functions defined the...and temperature. The convections for velocities and temperature are based on a mixed Gauss- -* Seidel and Jacobi schemes, proceeding from line-to...line according to the Gauss- Seidel scheme, updating values as each line is completed. With each line, however, the point-by-point iteration is based on

  19. Extended nonlinear feedback model for describing episodes of high inflation

    NASA Astrophysics Data System (ADS)

    Szybisz, Martín A.; Szybisz, Leszek

    2017-01-01

    An extension of the nonlinear feedback (NLF) formalism to describe regimes of hyper- and high-inflation in economy is proposed in the present work. In the NLF model the consumer price index (CPI) exhibits a finite time singularity of the type 1 /(tc - t) (1 - β) / β, with β > 0, predicting a blow up of the economy at a critical time tc. However, this model fails in determining tc in the case of weak hyperinflation regimes like, e.g., that occurred in Israel. To overcome this trouble, the NLF model is extended by introducing a parameter γ, which multiplies all terms with past growth rate index (GRI). In this novel approach the solution for CPI is also analytic being proportional to the Gaussian hypergeometric function 2F1(1 / β , 1 / β , 1 + 1 / β ; z) , where z is a function of β, γ, and tc. For z → 1 this hypergeometric function diverges leading to a finite time singularity, from which a value of tc can be determined. This singularity is also present in GRI. It is shown that the interplay between parameters β and γ may produce phenomena of multiple equilibria. An analysis of the severe hyperinflation occurred in Hungary proves that the novel model is robust. When this model is used for examining data of Israel a reasonable tc is got. High-inflation regimes in Mexico and Iceland, which exhibit weaker inflations than that of Israel, are also successfully described.

  20. A Miniature Magnetic-Force-Based Three-Axis AC Magnetic Sensor with Piezoelectric/Vibrational Energy-Harvesting Functions.

    PubMed

    Hung, Chiao-Fang; Yeh, Po-Chen; Chung, Tien-Kan

    2017-02-08

    In this paper, we demonstrate a miniature magnetic-force-based, three-axis, AC magnetic sensor with piezoelectric/vibrational energy-harvesting functions. For magnetic sensing, the sensor employs a magnetic-mechanical-piezoelectric configuration (which uses magnetic force and torque, a compact, single, mechanical mechanism, and the piezoelectric effect) to convert x -axis and y -axis in-plane and z -axis magnetic fields into piezoelectric voltage outputs. Under the x -axis magnetic field (sine-wave, 100 Hz, 0.2-3.2 gauss) and the z -axis magnetic field (sine-wave, 142 Hz, 0.2-3.2 gauss), the voltage output with the sensitivity of the sensor are 1.13-26.15 mV with 8.79 mV/gauss and 1.31-8.92 mV with 2.63 mV/gauss, respectively. In addition, through this configuration, the sensor can harness ambient vibrational energy, i.e., possessing piezoelectric/vibrational energy-harvesting functions. Under x -axis vibration (sine-wave, 100 Hz, 3.5 g) and z -axis vibration (sine-wave, 142 Hz, 3.8 g), the root-mean-square voltage output with power output of the sensor is 439 mV with 0.333 μW and 138 mV with 0.051 μW, respectively. These results show that the sensor, using this configuration, successfully achieves three-axis magnetic field sensing and three-axis vibration energy-harvesting. Due to these features, the three-axis AC magnetic sensor could be an important design reference in order to develop future three-axis AC magnetic sensors, which possess energy-harvesting functions, for practical industrial applications, such as intelligent vehicle/traffic monitoring, processes monitoring, security systems, and so on.

  1. A Miniature Magnetic-Force-Based Three-Axis AC Magnetic Sensor with Piezoelectric/Vibrational Energy-Harvesting Functions

    PubMed Central

    Hung, Chiao-Fang; Yeh, Po-Chen; Chung, Tien-Kan

    2017-01-01

    In this paper, we demonstrate a miniature magnetic-force-based, three-axis, AC magnetic sensor with piezoelectric/vibrational energy-harvesting functions. For magnetic sensing, the sensor employs a magnetic–mechanical–piezoelectric configuration (which uses magnetic force and torque, a compact, single, mechanical mechanism, and the piezoelectric effect) to convert x-axis and y-axis in-plane and z-axis magnetic fields into piezoelectric voltage outputs. Under the x-axis magnetic field (sine-wave, 100 Hz, 0.2–3.2 gauss) and the z-axis magnetic field (sine-wave, 142 Hz, 0.2–3.2 gauss), the voltage output with the sensitivity of the sensor are 1.13–26.15 mV with 8.79 mV/gauss and 1.31–8.92 mV with 2.63 mV/gauss, respectively. In addition, through this configuration, the sensor can harness ambient vibrational energy, i.e., possessing piezoelectric/vibrational energy-harvesting functions. Under x-axis vibration (sine-wave, 100 Hz, 3.5 g) and z-axis vibration (sine-wave, 142 Hz, 3.8 g), the root-mean-square voltage output with power output of the sensor is 439 mV with 0.333 μW and 138 mV with 0.051 μW, respectively. These results show that the sensor, using this configuration, successfully achieves three-axis magnetic field sensing and three-axis vibration energy-harvesting. Due to these features, the three-axis AC magnetic sensor could be an important design reference in order to develop future three-axis AC magnetic sensors, which possess energy-harvesting functions, for practical industrial applications, such as intelligent vehicle/traffic monitoring, processes monitoring, security systems, and so on. PMID:28208693

  2. Analytical study of fractional equations describing anomalous diffusion of energetic particles

    NASA Astrophysics Data System (ADS)

    Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

    2017-06-01

    To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

  3. High-temperature asymptotics of supersymmetric partition functions

    DOE PAGES

    Ardehali, Arash Arabi

    2016-07-05

    We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S 3 × S β 1, with S 3 the unit-radius squashed three-sphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around Smore » β 1. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R 3 × S 1. In theories where the effective potential is not positive semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, both believed to exhibit “misleading” anomaly matchings, and both believed to yield interacting superconformal field theories with c < a. Lastly, two new simple tests for dualities between 4d supersymmetric gauge theories emerge as byproducts of our analysis.« less

  4. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    NASA Astrophysics Data System (ADS)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  5. Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes

    NASA Astrophysics Data System (ADS)

    Ma, Hong; Li, Jin

    2018-04-01

    In this paper, we describe quasinormal modes (QNMs) for gravitational perturbations of Einstein-Gauss-Bonnet black holes (BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime (flat, de Sitter (dS) and anti-de Sitter (AdS)). Our attention is concentrated on discussing the (in)stability of Einstein-Gauss-Bonnet AdS BHs through the temporal evolution of all types of gravitational perturbation fields (tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore, the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet AdS BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet AdS BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds. Supported by FAPESP (2012/08934-0), National Natural Science Foundation of China (11205254, 11178018, 11375279, 11605015), the Natural Science Foundation Project of CQ CSTC (2011BB0052), and the Fundamental Research Funds for the Central Universities (106112016CDJXY300002, 106112017CDJXFLX0014, CDJRC10300003)

  6. Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brihaye, Yves; Hartmann, Betti

    We study the stability of static, hyperbolic Gauss-Bonnet black holes in (4+1)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of AdS{sub 2}xH{sup 3} such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field thatmore » possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.« less

  7. Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

    PubMed

    Matsuzaki, Rei; Yabushita, Satoshi

    2017-09-05

    Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  8. Maximum of the modulus of kernels in Gauss-Turan quadratures

    NASA Astrophysics Data System (ADS)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.

    2008-06-01

    We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32

  9. A family of analytic equilibrium solutions for the Grad-Shafranov equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Guazzotto, L.; Freidberg, J. P.

    2007-11-15

    A family of exact solutions to the Grad-Shafranov equation, similar to those described by Atanasiu et al. [C. V. Atanasiu, S. Guenter, K. Lackner, and I. G. Miron, Phys. Plasmas 11, 3510 (2004)], is presented. The solution allows for finite plasma aspect ratio, elongation and triangularity, while only requiring the evaluation of a small number of well-known hypergeometric functions. Plasma current, pressure, and pressure gradients are set to zero at the plasma edge. Realistic equilibria for standard and spherical tokamaks are presented.

  10. Coupling coefficients for tensor product representations of quantum SU(2)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

    2014-10-15

    We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

  11. A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

    NASA Astrophysics Data System (ADS)

    F, Khannous; A, A. A. Ebrahim; A, Belafhal

    2016-04-01

    Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

  12. Development in understanding of Gauss-Krüger projection and its outcomes

    NASA Astrophysics Data System (ADS)

    Masaharu, Hiroshi

    2018-05-01

    The role of Gauss and Krüger is made clear in developing Gauss-Krüger projection. Gauss developed the projection and Krüger had brought Gauss's posthumous work into the open. From studying such historical issues, useful projection formula was found and this is now implemented for actual usage in surveying in Japan.

  13. Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

    PubMed

    Kiselev, Aleksei P; Plachenov, Alexandr B

    2016-04-01

    The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

  14. Explicit densities of multidimensional ballistic Lévy walks.

    PubMed

    Magdziarz, Marcin; Zorawik, Tomasz

    2016-08-01

    Lévy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real-life phenomena. In this paper we derive explicit formulas for densities of the two- (2D) and three-dimensional (3D) ballistic Lévy walks, which are most important in applications. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D Lévy walks are expressed in terms of hypergeometric functions and the right-side Riemann-Liouville fractional derivative, which allows us to efficiently evaluate them numerically. The theoretical results agree perfectly with Monte Carlo simulations.

  15. The elastic field induced by a hemispherical inclusion in the half-space

    NASA Astrophysics Data System (ADS)

    Wu, Linzhi

    2003-06-01

    The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry ( x 3-axis).

  16. Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes

    NASA Astrophysics Data System (ADS)

    Pasquetti, Richard; Rapetti, Francesca

    2017-10-01

    In a recent JCP paper [9], a higher order triangular spectral element method (TSEM) is proposed to address seismic wave field modeling. The main interest of this TSEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that, similarly to the usual SEM (say QSEM), the basis functions are Lagrange polynomials based on a set of points that shows both nice interpolation and quadrature properties. In the quadrangle, i.e. for the QSEM, the set of points is simply obtained by tensorial product of Gauss-Lobatto-Legendre (GLL) points. In the triangle, finding such an appropriate set of points is however not trivial. Thus, the work of [9] follows anterior works that started in 2000's [2,6,11] and now provides cubature nodes and weights up to N = 9, where N is the total degree of the polynomial approximation. Here we wish to evaluate the accuracy of this cubature nodes TSEM with respect to the Fekete-Gauss one, see e.g.[12], that makes use of two sets of points, namely the Fekete points and the Gauss points of the triangle for interpolation and quadrature, respectively. Because the Fekete-Gauss TSEM is in the spirit of any nodal hp-finite element methods, one may expect that the conclusions of this Note will remain relevant if using other sets of carefully defined interpolation points.

  17. A new molecular evolution model for limited insertion independent of substitution.

    PubMed

    Lèbre, Sophie; Michel, Christian J

    2013-10-01

    We recently introduced a new molecular evolution model called the IDIS model for Insertion Deletion Independent of Substitution [13,14]. In the IDIS model, the three independent processes of substitution, insertion and deletion of residues have constant rates. In order to control the genome expansion during evolution, we generalize here the IDIS model by introducing an insertion rate which decreases when the sequence grows and tends to 0 for a maximum sequence length nmax. This new model, called LIIS for Limited Insertion Independent of Substitution, defines a matrix differential equation satisfied by a vector P(t) describing the sequence content in each residue at evolution time t. An analytical solution is obtained for any diagonalizable substitution matrix M. Thus, the LIIS model gives an expression of the sequence content vector P(t) in each residue under evolution time t as a function of the eigenvalues and the eigenvectors of matrix M, the residue insertion rate vector R, the total insertion rate r, the initial and maximum sequence lengths n0 and nmax, respectively, and the sequence content vector P(t0) at initial time t0. The derivation of the analytical solution is much more technical, compared to the IDIS model, as it involves Gauss hypergeometric functions. Several propositions of the LIIS model are derived: proof that the IDIS model is a particular case of the LIIS model when the maximum sequence length nmax tends to infinity, fixed point, time scale, time step and time inversion. Using a relation between the sequence length l and the evolution time t, an expression of the LIIS model as a function of the sequence length l=n(t) is obtained. Formulas for 'insertion only', i.e. when the substitution rates are all equal to 0, are derived at evolution time t and sequence length l. Analytical solutions of the LIIS model are explicitly derived, as a function of either evolution time t or sequence length l, for two classical substitution matrices: the 3-parameter symmetric substitution matrix [12] (LIIS-SYM3) and the HKY asymmetric substitution matrix[9] (LIIS-HKY). An evaluation of the LIIS model (precisely, LIIS-HKY) based on four statistical analyses of the GC content in complete genomes of four prokaryotic taxonomic groups, namely Chlamydiae, Crenarchaeota, Spirochaetes and Thermotogae, shows the expected improvement from the theory of the LIIS model compared to the IDIS model. Copyright © 2013 Elsevier Inc. All rights reserved.

  18. Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

    PubMed

    Bajnok, Zoltán; Balog, János; Ito, Katsushi; Satoh, Yuji; Tóth, Gábor Zsolt

    2016-05-06

    We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

  19. Quasinormal modes of the BTZ black hole under scalar perturbations with a non-minimal coupling: exact spectrum

    NASA Astrophysics Data System (ADS)

    Panotopoulos, Grigoris

    2018-06-01

    We perturb the non-rotating BTZ black hole with a non-minimally coupled massless scalar field, and we compute the quasinormal spectrum exactly. We solve the radial equation in terms of hypergeometric functions, and we obtain an analytical expression for the quasinormal frequencies. In addition, we compare our analytical results with the 6th order semi-analytical WKB method, and we find an excellent agreement. The impact of the nonminimal coupling as well as of the cosmological constant on the quasinormal spectrum is briefly discussed.

  20. On the arbitrary l-wave solutions of the deformed hyperbolic manning-rosen potential including an improved approximation to the orbital centrifugal term

    NASA Astrophysics Data System (ADS)

    Xu, Chun-Long; Zhang, Min-Cang

    2017-01-01

    The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

  1. Some Remarks on Solutions of Fermats Last Equation in Terms of Wright’s Hypergeometric Function

    DTIC Science & Technology

    1990-02-16

    DISTRIBUTION/AVAILABILITY OF ABSTRACT 121 ABSTRACT SECURITY CLASSIFICATION MUNCLASSIFIED/UNLIMITED C SAME AS RPT 0 DTIC USERS UNCLASSIFIED 22a NAME...A) = (u/vl)", 4’ C \\) = (U/V)%, then from Lemma 2 we have (UsV2)n + (U2VI )n = V2) and the theorem is proved. ANOTHER DERIVATION OF EQ. (10) From Eq. (3... Ramanujan (7, pp. 71, 307] studied and derived solutions of trinonials in Chapter 3 of his notebooks (1903-1914) and in his first quarterly report

  2. MAGNETO-ACOUSTIC WAVES IN A GRAVITATIONALLY STRATIFIED MAGNETIZED PLASMA: EIGEN-SOLUTIONS AND THEIR APPLICATIONS TO THE SOLAR ATMOSPHERE

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mather, J. F.; Erdélyi, R., E-mail: robertus@sheffield.ac.uk

    2016-05-10

    Magneto-acoustic gravity (MAG) waves have been studied intensively in the context of astrophysical plasmas. There are three popular choices of analytic modeling using a Cartesian coordinate system: a magnetic field parallel, perpendicular, or at an angle to the gravitational field. Here, we study a gravitationally stratified plasma embedded in a parallel, so called vertical, magnetic field. We find a governing equation for the auxiliary quantity Θ = p {sub 1}/ ρ {sub 0}, and find solutions in terms of hypergeometric functions. With the convenient relationship between Θ and the vertical velocity component, v {sub z}, we derive the solution formore » v{sub z}. We show that the four linearly independent functions for v{sub z} can also be cast as single hypergeometric functions, rather than the Frobenius series derived by Leroy and Schwartz. We are then able to analyze a case of approximation for a one-layer solution, taking the small wavelength limit. Motivated by solar atmospheric applications, we finally commence study of the eigenmodes of perturbations for a two-layer model using our solutions, solving the dispersion relation numerically. We show that, for a transition between a photospheric and chromospheric plasma embedded in a vertical magnetic field, modes exist that are between the observationally widely investigated three and five minute oscillation periods, interpreted as solar global oscillations in the lower solar atmosphere . It is also shown that, when the density contrast between the layers is large (e.g., applied to photosphere/chromosphere-corona), the global eigenmodes are practically a superposition of the same as in each of the separate one-layer systems.« less

  3. Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

    NASA Astrophysics Data System (ADS)

    Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

    2018-04-01

    We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

  4. Classes of exact Einstein Maxwell solutions

    NASA Astrophysics Data System (ADS)

    Komathiraj, K.; Maharaj, S. D.

    2007-12-01

    We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

  5. Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

    NASA Astrophysics Data System (ADS)

    Thirukkanesh, S.; Ragel, F. C.

    2014-04-01

    We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

  6. Hypergeometric Forms for Ising-Class Integrals

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bailey, David H.; Borwein, David; Borwein, Jonathan M.

    2006-07-01

    We apply experimental-mathematical principles to analyzecertain integrals relevant to the Ising theory of solid-state physics. Wefind representations of the these integrals in terms of MeijerG-functions and nested-Barnes integrals. Our investigations began bycomputing 500-digit numerical values of Cn,k,namely a 2-D array of Isingintegrals for all integers n, k where n is in [2,12]and k is in [0,25].We found that some Cn,k enjoy exact evaluations involving DirichletL-functions or the Riemann zeta function. In theprocess of analyzinghypergeometric representations, we found -- experimentally and strikingly-- that the Cn,k almost certainly satisfy certain inter-indicialrelations including discrete k-recursions. Using generating functions,differential theory, complex analysis, and Wilf-Zeilbergermore » algorithms weare able to prove some central cases of these relations.« less

  7. Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

    2016-02-15

    Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

  8. Virtual source for a Mathieu-Gauss beam

    NASA Astrophysics Data System (ADS)

    Dan, Li; Zhijun, Ren; Suyu, Deng

    2017-05-01

    We introduce a group of virtual sources for generating 2nth-order even Mathieu-Gauss beams based on the beam superposition. Integral and differential representations are derived for a 2nth-order even Mathieu-Gauss wave and the solution yields a corresponding 2nth-order even paraxial Mathieu-Gauss beam in an appropriate limit. The first three orders of nonparaxial corrections for the on-axis field of the 2nth-order even paraxial Mathieu-Gauss beam are obtained using the integral representation.

  9. Density reconstruction in multiparameter elastic full-waveform inversion

    NASA Astrophysics Data System (ADS)

    Sun, Min'ao; Yang, Jizhong; Dong, Liangguo; Liu, Yuzhu; Huang, Chao

    2017-12-01

    Elastic full-waveform inversion (EFWI) is a quantitative data fitting procedure that recovers multiple subsurface parameters from multicomponent seismic data. As density is involved in addition to P- and S-wave velocities, the multiparameter EFWI suffers from more serious tradeoffs. In addition, compared with P- and S-wave velocities, the misfit function is less sensitive to density perturbation. Thus, a robust density reconstruction remains a difficult problem in multiparameter EFWI. In this paper, we develop an improved scattering-integral-based truncated Gauss-Newton method to simultaneously recover P- and S-wave velocities and density in EFWI. In this method, the inverse Gauss-Newton Hessian has been estimated by iteratively solving the Gauss-Newton equation with a matrix-free conjugate gradient algorithm. Therefore, it is able to properly handle the parameter tradeoffs. To give a detailed illustration of the tradeoffs between P- and S-wave velocities and density in EFWI, wavefield-separated sensitivity kernels and the Gauss-Newton Hessian are numerically computed, and their distribution characteristics are analyzed. Numerical experiments on a canonical inclusion model and a modified SEG/EAGE Overthrust model have demonstrated that the proposed method can effectively mitigate the tradeoff effects, and improve multiparameter gradients. Thus, a high convergence rate and an accurate density reconstruction can be achieved.

  10. Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

    NASA Astrophysics Data System (ADS)

    Wu, Leyuan

    2018-01-01

    We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.

  11. Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple q-series identities

    NASA Astrophysics Data System (ADS)

    Zhang, Zhizheng; Wang, Tianze

    2008-07-01

    In this paper, we first give several operator identities involving the bivariate Rogers-Szegö polynomials. By applying the technique of parameter augmentation to the multiple q-binomial theorems given by Milne [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, AdvE Math. 131 (1997) 93-187], we obtain several new multiple q-series identities involving the bivariate Rogers-Szegö polynomials. These include multiple extensions of Mehler's formula and Rogers's formula. Our U(n+1) generalizations are quite natural as they are also a direct and immediate consequence of their (often classical) known one-variable cases and Milne's fundamental theorem for An or U(n+1) basic hypergeometric series in Theorem 1E49 of [S.C. Milne, An elementary proof of the Macdonald identities for , Adv. Math. 57 (1985) 34-70], as rewritten in Lemma 7.3 on p. 163 of [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93-187] or Corollary 4.4 on pp. 768-769 of [S.C. Milne, M. Schlosser, A new An extension of Ramanujan's summation with applications to multilateral An series, Rocky Mountain J. Math. 32 (2002) 759-792].

  12. Unique Properties and Prospects: Quantum Theory of the Orbital Angular Momentum of Ince-Gauss Beams

    NASA Astrophysics Data System (ADS)

    Plick, William; Krenn, Mario; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton

    2012-02-01

    The Ince-Gauss modes represent a new addition to the standard solutions to the paraxial wave equation. Parametrized by the ellipticity of the beam, they span the solution space between the Hermite-Gauss and the Laguerre-Gauss modes. These beams may be decomposed in either basis, and single photons in the Ince-Gauss modes exist naturally as superpositions of either Laguerre-Gauss or Hermite-Gauss modes. We present the fully quantum theory of the orbital angular momentum of these beams. Interesting features that arise are: stable beams with fractional orbital angular momentum, non-monotonic behavior of the OAM with respect to ellipticity, and the possibility of orthogonal modes possessing the same OAM. We believe that these modes may open up a fully new parameter space for quantum informatics and communication, and thus are worthy of thorough study.

  13. Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds

    NASA Astrophysics Data System (ADS)

    Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung

    2016-06-01

    We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

  14. Quantum Hurwitz numbers and Macdonald polynomials

    NASA Astrophysics Data System (ADS)

    Harnad, J.

    2016-11-01

    Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

  15. Construction of normal-regular decisions of Bessel typed special system

    NASA Astrophysics Data System (ADS)

    Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

    2017-09-01

    Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

  16. Notes on integral identities for 3d supersymmetric dualities

    NASA Astrophysics Data System (ADS)

    Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta

    2018-04-01

    Four dimensional N=2 Argyres-Douglas theories have been recently conjectured to be described by N=1 Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian N=4 theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A 2 n-1 case via hyperbolic hypergeometric integrals. We study the D 4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.

  17. Linear dispersion properties of ring velocity distribution functions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Vandas, Marek, E-mail: marek.vandas@asu.cas.cz; Hellinger, Petr; Institute of Atmospheric Physics, AS CR, Bocni II/1401, CZ-14100 Prague

    2015-06-15

    Linear properties of ring velocity distribution functions are investigated. The dispersion tensor in a form similar to the case of a Maxwellian distribution function, but for a general distribution function separable in velocities, is presented. Analytical forms of the dispersion tensor are derived for two cases of ring velocity distribution functions: one obtained from physical arguments and one for the usual, ad hoc ring distribution. The analytical expressions involve generalized hypergeometric, Kampé de Fériet functions of two arguments. For a set of plasma parameters, the two ring distribution functions are compared. At the parallel propagation with respect to the ambientmore » magnetic field, the two ring distributions give the same results identical to the corresponding bi-Maxwellian distribution. At oblique propagation, the two ring distributions give similar results only for strong instabilities, whereas for weak growth rates their predictions are significantly different; the two ring distributions have different marginal stability conditions.« less

  18. A New Family of Solvable Pearson-Dirichlet Random Walks

    NASA Astrophysics Data System (ADS)

    Le Caër, Gérard

    2011-07-01

    An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

  19. A Converse of a Result about the Floor Function by Hermite

    ERIC Educational Resources Information Center

    Mortici, Cristinel

    2012-01-01

    The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

  20. A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

    2008-05-15

    We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

  1. Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime: exact spectrum

    NASA Astrophysics Data System (ADS)

    Destounis, Kyriakos; Panotopoulos, Grigoris; Rincón, Ángel

    2018-02-01

    We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordström black hole is observed.

  2. Fractional dynamics using an ensemble of classical trajectories

    NASA Astrophysics Data System (ADS)

    Sun, Zhaopeng; Dong, Hao; Zheng, Yujun

    2018-01-01

    A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (F11) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.

  3. Colon Cancer Risk Assessment - Gauss Program

    Cancer.gov

    An executable file (in GAUSS) that projects absolute colon cancer risk (with confidence intervals) according to NCI’s Colorectal Cancer Risk Assessment Tool (CCRAT) algorithm. GAUSS is not needed to run the program.

  4. Hipergeometric solutions to some nonhomogeneous equations of fractional order

    NASA Astrophysics Data System (ADS)

    Olivares, Jorge; Martin, Pablo; Maass, Fernando

    2017-12-01

    In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

  5. Vector-beam solutions of Maxwell's wave equation.

    PubMed

    Hall, D G

    1996-01-01

    The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

  6. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    NASA Astrophysics Data System (ADS)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-07-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

  7. Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

    PubMed

    Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

    2017-07-01

    For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

  8. A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals.

    PubMed

    Kotini, A; Anninos, P; Anastasiadis, A N; Tamiolakis, D

    2005-09-07

    The aim of this study was to compare a theoretical neural net model with MEG data from epileptic patients and normal individuals. Our experimental study population included 10 epilepsy sufferers and 10 healthy subjects. The recordings were obtained with a one-channel biomagnetometer SQUID in a magnetically shielded room. Using the method of x2-fitting it was found that the MEG amplitudes in epileptic patients and normal subjects had Poisson and Gauss distributions respectively. The Poisson connectivity derived from the theoretical neural model represents the state of epilepsy, whereas the Gauss connectivity represents normal behavior. The MEG data obtained from epileptic areas had higher amplitudes than the MEG from normal regions and were comparable with the theoretical magnetic fields from Poisson and Gauss distributions. Furthermore, the magnetic field derived from the theoretical model had amplitudes in the same order as the recorded MEG from the 20 participants. The approximation of the theoretical neural net model with real MEG data provides information about the structure of the brain function in epileptic and normal states encouraging further studies to be conducted.

  9. On reinitializing level set functions

    NASA Astrophysics Data System (ADS)

    Min, Chohong

    2010-04-01

    In this paper, we consider reinitializing level functions through equation ϕt+sgn(ϕ0)(‖∇ϕ‖-1)=0[16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation. We compare the three temporal discretizations: the second order Runge-Kutta method, the forward Euler method, and a Gauss-Seidel iteration of the forward Euler method. The fact that the time in the equation is fictitious makes a hypothesis that all the temporal discretizations result in the same result in their stationary states. The fact that the absolute stability region of the forward Euler method is not wide enough to include all the eigenvalues of the linearized semi-discrete system of the second order ENO spatial discretization makes another hypothesis that the forward Euler temporal discretization should invoke numerical instability. Our results in this paper contradict both the hypotheses. The Runge-Kutta and Gauss-Seidel methods obtain the second order accuracy, and the forward Euler method converges with order between one and two. Examining all their properties, we conclude that the Gauss-Seidel method is the best among the three. Compared to the Runge-Kutta, it is twice faster and requires memory two times less with the same accuracy.

  10. Experimental generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase holograms

    NASA Astrophysics Data System (ADS)

    Mellado-Villaseñor, Gabriel; Aguirre-Olivas, Dilia; Sánchez-de-la-Llave, David; Arrizón, Victor

    2015-08-01

    We generate Hermite-Gauss and Ince-Gauss beams by using kinoform phase holograms encoded onto a liquid crystal display. The phase transmittance of this holograms coincide with the phases of such beams. Scale versions of the desired beams appear at the Fourier domain of the KPHs. When an appropriated pupil size is employed, the method synthesizes HG and IG beams with relatively high accuracy and high efficiency. It is noted that experimental and numerical results are agreement with the theory.

  11. Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

    NASA Astrophysics Data System (ADS)

    Da Rocha, R.; Capelas Oliveira, E.

    2009-01-01

    The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

  12. Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

    NASA Astrophysics Data System (ADS)

    Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

    2018-01-01

    Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

  13. Evolution of spherical cavitation bubbles: Parametric and closed-form solutions

    NASA Astrophysics Data System (ADS)

    Mancas, Stefan C.; Rosu, Haret C.

    2016-02-01

    We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel's equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integration.

  14. Elliptic Integrals in the Minkowski Plane

    DTIC Science & Technology

    1991-05-09

    factorial Pochhammer notation F(a + k) (a)k - (a) Let F(a, b , c denote the hypergeometric function. Assume c - a - b = d , where d is a positive...integer. Then in a neighborhood of C = 1 , ((d) F(a+ b+d) d-1 (a)n (b)n )n(22) F(a , b , a + b + d , () = E~ )rb+ 0-’)n( ) r(a +d) r(b +d) n =O0( ’d’ n...axes a , b and eccentriaty e = c where c = Ta2 - b2 . Let P denote one of the foci of the ellipse. Then (26) 1 1 1 2 and(26) ar+(K, P) 2 -er F(- 1

  15. Studies on the Reduction of Intermodulation Generation in Communications Systems

    DTIC Science & Technology

    1980-07-07

    AGENCY NAME & ADDRESS(ff dillfetmn from Controlling Office) IS. SECURITY CLASS. (of this report) Unclassified ISO . DECLASSIFICATION DOWNGRAD-ING SCHEDULE...FIELD 40GAUSS 120 GAUSS ISO GAUSS 340 GAUSS 1MG OSCILLOGRAMS OF 񓰨’ STAINLESS STEEL ADAPTER (SAMPLE A WITH EXTERNAL 2kHz AC MAGNETIC FIELD I PEAK...34P1 (,I P,2 -90- 7.07 GC; 0 V - iSo . .. _ 3D -100- AL(N23> ,-J/ -OLD/ / / OF-110 . O/ 070> V(HNS)// 2 -120 A(3080) , -i0.22 AL( NP) . / AG (H SI

  16. The time delay in strong gravitational lensing with Gauss-Bonnet correction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Man, Jingyun; Cheng, Hongbo, E-mail: jingyunman@mail.ecust.edu.cn, E-mail: hbcheng@ecust.edu.cn

    2014-11-01

    The time delay between two relativistic images in the strong gravitational lensing governed by Gauss-Bonnet gravity is studied. We make a complete analytical derivation of the expression of time delay in presence of Gauss-Bonnet coupling. With respect to Schwarzschild, the time delay decreases as a consequence of the shrinking of the photon sphere. As the coupling increases, the second term in the time delay expansion becomes more relevant. Thus time delay in strong limit encodes some new information about geometry in five-dimensional spacetime with Gauss-Bonnet correction.

  17. Entanglement of Ince-Gauss Modes of Photons

    NASA Astrophysics Data System (ADS)

    Krenn, Mario; Fickler, Robert; Plick, William; Lapkiewicz, Radek; Ramelow, Sven; Zeilinger, Anton

    2012-02-01

    Ince-Gauss modes are solutions of the paraxial wave equation in elliptical coordinates [1]. They are natural generalizations both of Laguerre-Gauss and of Hermite-Gauss modes, which have been used extensively in quantum optics and quantum information processing over the last decade [2]. Ince-Gauss modes are described by one additional real parameter -- ellipticity. For each value of ellipticity, a discrete infinite-dimensional Hilbert space exists. This conceptually new degree of freedom could open up exciting possibilities for higher-dimensional quantum optical experiments. We present the first entanglement of non-trivial Ince-Gauss Modes. In our setup, we take advantage of a spontaneous parametric down-conversion process in a non-linear crystal to create entangled photon pairs. Spatial light modulators (SLMs) are used as analyzers. [1] Miguel A. Bandres and Julio C. Guti'errez-Vega ``Ince Gaussian beams", Optics Letters, Vol. 29, Issue 2, 144-146 (2004) [2] Adetunmise C. Dada, Jonathan Leach, Gerald S. Buller, Miles J. Padgett, and Erika Andersson, ``Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities", Nature Physics 7, 677-680 (2011)

  18. Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

    NASA Astrophysics Data System (ADS)

    Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

    2018-05-01

    We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

  19. Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yükçü, Niyazi

    Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

  20. Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

    NASA Astrophysics Data System (ADS)

    Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R.

    2017-06-01

    This paper is intended to provide exponentially accurate Galerkin, Petrov-Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre-Gauss and Laguerre-Gauss-Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov-Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov-Galerkin methods are listed at the end.

  1. Scalar field collapse in Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Banerjee, Narayan; Paul, Tanmoy

    2018-02-01

    We consider a "scalar-Einstein-Gauss-Bonnet" theory in four dimension, where the scalar field couples non-minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from the exterior by an apparent horizon.

  2. The Tortured History of Gauss's Law

    NASA Astrophysics Data System (ADS)

    Spencer, Ross

    2009-10-01

    American physics textbooks contain the following equation, which is called Gauss's law: E .d S = qenclosed ɛ0 It is odd, however, that biographies of Karl Friedrich Gauss (1777-1855) contain no mention of this law. A brief history of this important result will be presented in which it will be shown that what we call Gauss's law today was originally guessed at by Joseph Priestly (1733-1804) after he read a letter from Benjamin Franklin (1706-1790), then was derived, forgotten, and re-derived several times in two different contexts by many of the luminaries of physics in the eighteenth and nineteenth centuries.

  3. Numerical study on the selective excitation of Helmholtz-Gauss beams in end-pumped solid-state digital lasers with the control of the laser gain transverse position provided by off-axis end pumping

    NASA Astrophysics Data System (ADS)

    Tsai, Ko-Fan; Chu, Shu-Chun

    2018-03-01

    This study proposes a complete and unified method for selective excitation of any specified nearly nondiffracting Helmholtz-Gauss (HzG) beam in end-pumped solid-state digital lasers. Four types of the HzG beams: cosine-Gauss beams, Bessel-Gauss beams, Mathieu-Gauss beams, and, in particular, parabolic-Gauss beams are successfully demonstrated to be generated with the proposed methods. To the best of the authors’ knowledge, parabolic-Gauss beams have not yet been directly generated from any kind of laser system. The numerical results of this study show that one can successfully achieve any lasing HzG beams directly from the solid-state digital lasers with only added control of the laser gain transverse position provided by off-axis end pumping. This study also presents a practical digital laser set-up for easily manipulating off-axis pumping in order to achieve the control of the laser gain transverse gain position in digital lasers. The reported results in this study provide advancement of digital lasers in dynamically generating nondiffracting beams. The control of the digital laser cavity gain position creates the possibility of achieving real-time selection of more laser modes in digital lasers, and it is worth further investigation in the future.

  4. On temporal connectivity of PFC via Gauss-Markov modeling of fNIRS signals.

    PubMed

    Aydöre, Sergül; Mihçak, M Kivanç; Ciftçi, Koray; Akin, Ata

    2010-03-01

    Functional near-infrared spectroscopy (fNIRS) is an optical imaging method, which monitors the brain activation by measuring the successive changes in the concentration of oxy- and deoxyhemoglobin in real time. In this study, we present a method to investigate the functional connectivity of prefrontal cortex (PFC) Sby applying a Gauss-Markov model to fNIRS signals. The hemodynamic changes on PFC during the performance of cognitive paradigm are measured by fNIRS for 17 healthy adults. The color-word matching Stroop task is performed to activate 16 different regions of PFC. There are three different types of stimuli in this task, which can be listed as incongruent stimulus (IS), congruent stimulus (CS), and neutral stimulus (NS), respectively. We introduce a new measure, called "information transfer metric" (ITM) for each time sample. The behavior of ITMs during IS are significantly different from the ITMs during CS and NS, which is consistent with the outcome of the previous research, which concentrated on fNIRS signal analysis via color-word matching Stroop task. Our analysis shows that the functional connectivity of PFC is highly relevant with the cognitive load, i.e., functional connectivity increases with the increasing cognitive load.

  5. Three friendly walkers

    NASA Astrophysics Data System (ADS)

    Jensen, Iwan

    2017-01-01

    More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

  6. Research on atmospheric transmission distortion of Gauss laser using multiple phase screen method

    NASA Astrophysics Data System (ADS)

    Zhang, Yizhuo; Wang, Qiushi; Gu, Haidong

    2018-02-01

    The laser beam is attenuated, broadened, defocused and may even be deflected from its initial propagation direction as it propagates through the atmosphere. It leads to the decrease of the laser intensity of the receiving surface. Gauss beam is the fundamental components of all possible laser waveforms. Therefore, research on the transmission of the Gauss laser has far-reaching consequences in optical communication, weaponry, target designation, ranging, remote sensing and other applications that require transmission of laser beams through the atmosphere. In this paper, we propose a laboratory simulation method using multi-phase screen to calculate the effects of atmospheric turbulence. Theoretical analysis of Gauss laser transmission in the atmosphere is given. By calculating the propagation of the Gauss beam TEM00, the far field intensity and phase distribution is shown. By the given method, the optical setup is presented and used for optimizing the adaptive optics algorithm.

  7. Radiating black hole solutions in Einstein-Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dominguez, Alfredo E.; Instituto Universitario Aeronautico, Avenida Fuerza Aerea km 6.5.; Gallo, Emanuel

    2006-03-15

    In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditionsmore » on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.« less

  8. Propagation of partially coherent Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Zhao, Chengliang; Cai, Yangjian

    2011-05-01

    Based on the generalized Huygens-Fresnel integral, propagation of partially coherent Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere was investigated. Analytical propagation formulae were derived for the cross-spectral densities of partially coherent Lorentz and Lorentz-Gauss beams. As an application example, the focusing properties of partially coherent Gaussian, Lorentz and Lorentz-Gauss beams in a turbulent atmosphere and in free space were studied numerically and comparatively. It is found that the focusing properties of such beams are closely related to the initial coherence length and the structure constant of turbulence. By choosing a suitable initial coherence length, a partially coherent Lorentz beam can be focused more tightly than a Gaussian or Lorentz-Gauss beam in free space or in a turbulent atmosphere with small structure constant at the geometrical focal plane.

  9. Contributions on Optimizing Approximations in the Study of Melting and Solidification Processes That Occur in Processing by Electro-Erosion

    NASA Astrophysics Data System (ADS)

    Potra, F. L.; Potra, T.; Soporan, V. F.

    We propose two optimization methods of the processes which appear in EDM (Electrical Discharge Machining). First refers to the introduction of a new function approximating the thermal flux energy in EDM machine. Classical researches approximate this energy with the Gauss' function. In the case of unconventional technology the Gauss' bell became null only for r → +∞, where r is the radius of crater produced by EDM. We introduce a cubic spline regression which descends to zero at the crater's boundary. In the second optimization we propose modifications in technologies' work regarding the displacement of the tool electrode to the piece electrode such that the material melting to be realized in optimal time and the feeding speed with dielectric liquid regarding the solidification of the expulsed material. This we realize using the FAHP algorithm based on the theory of eigenvalues and eigenvectors, which lead to mean values of best approximation. [6

  10. Quadrature imposition of compatibility conditions in Chebyshev methods

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Streett, C. L.

    1990-01-01

    Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

  11. Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole

    NASA Astrophysics Data System (ADS)

    Zhang, Cheng-Yong; Li, Peng-Cheng; Chen, Bin

    2018-02-01

    We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and nonminimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the nonminimally coupling constant, the spacetime dimension, the cosmological constant, and the Gauss-Bonnet coefficient in detail. We find that the nonminimal coupling may suppress the greybody factor and the Gauss-Bonnet coupling could enhance it, but they both suppress the energy emission rate of Hawking radiation.

  12. Rows of optical vortices from elliptically perturbing a high-order beam

    NASA Astrophysics Data System (ADS)

    Dennis, Mark R.

    2006-05-01

    An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.

  13. Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hu Yapeng; Sun Peng; Zhang Jianhui

    2011-06-15

    Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of the Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity {eta}, entropy density s, thermal conductivity {kappa} and electrical conductivity {sigma}. However, it does not affect themore » so-called Wiedemann-Franz law which relates {kappa} to {sigma}, while it affects the ratio {eta}/s. In addition, another interesting result is that {eta}/s can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.« less

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dehghani, M.H.; Department of Physics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1; Perimeter Institute for Theoretical Physics, 35 Caroline Street North, Waterloo, Ontario

    We investigate the existence of Taub-NUT (Newman-Unti-Tamburino) and Taub-bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r=N, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter {alpha} goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield nonextremal NUT solutions to Einstein gravity having a curvature singularity at r=N in the limit {alpha}{yields}0. Indeed, we have nonextreme NUT solutions in 2+2k dimensions withmore » nontrivial fibration only when the 2k-dimensional base space is chosen to be CP{sup 2k}. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a two-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two-dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at r=N. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.« less

  15. Vacuum polarization in Coulomb field revisited

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz; Šimsa, D.

    2017-04-15

    Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonicmore » hydrogen the result obtained here reasonably agrees with that given in literature.« less

  16. Conformable derivative approach to anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Zhou, H. W.; Yang, S.; Zhang, S. Q.

    2018-02-01

    By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

  17. Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

    NASA Astrophysics Data System (ADS)

    Sberna, Laura; Pani, Paolo

    2017-12-01

    It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

  18. Aurora on Uranus - A Faraday disc dynamo mechanism

    NASA Technical Reports Server (NTRS)

    Hill, T. W.; Rassbach, M. E.; Dessler, A. J.

    1983-01-01

    A mechanism is proposed whereby the solar wind flowing past the magnetosphere of Uranus causes a Faraday disk dynamo topology to be established and power to be extracted from the kinetic energy of rotation of Uranus. An immediate consequence of this dynamo is the generation of Birkeland currents that flow in and out of the sunlit polar cap with the accompanying production of polar aurora. The power extracted from planetary rotation is calculated as a function of planetary dipole magnetic moment and the ionospheric conductivity of Uranus. For plausible values of ionospheric conductivity, the observed auroral power requires a magnetic moment corresponding to a surface equatorial field of the order of 4 Gauss, slightly larger than the value 1.8 Gauss given by the empirical 'magnetic Bodes law'.

  19. Product of Ginibre matrices: Fuss-Catalan and Raney distributions

    NASA Astrophysics Data System (ADS)

    Penson, Karol A.; Życzkowski, Karol

    2011-06-01

    Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

  20. Product of Ginibre matrices: Fuss-Catalan and Raney distributions.

    PubMed

    Penson, Karol A; Zyczkowski, Karol

    2011-06-01

    Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

  1. Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency

    DTIC Science & Technology

    2010-01-01

    sgn(Y )C log n, o.w, (45b) where sgn is the sign function and C > 0 is a constant. Consider the functionals H ′2, φ ′ 2 by replacing Yn with Zn in H2...Gaussian signal processing, and has held visiting faculty positions at INP , Toulouse. He is currently with the US Army Research Laboratory where his work

  2. Numerical Computation of Subsonic Conical Diffuser Flows with Nonuniform Turbulent Inlet Conditions

    DTIC Science & Technology

    1977-09-01

    Gauss - Seidel Point Iteration Method . . . . . . . . . . . . . . . 7.0 FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT...can be solved in several ways. For simplicity, a standard Gauss - Seidel iteration method is used to obtain the solution . The method updates the...FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT ITERATION ,ŘETHOD The advantage of using the Gauss - Seidel point iteration method to

  3. Wave equations in conformal gravity

    NASA Astrophysics Data System (ADS)

    Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

    2018-05-01

    We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

  4. Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

    NASA Astrophysics Data System (ADS)

    Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

    2017-12-01

    A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

  5. Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

    NASA Astrophysics Data System (ADS)

    Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

    2018-06-01

    A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

  6. Electron-pair-production cross section in the tip region of the positron spectrum

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sud, K.K.; Sharma, D.K.

    1984-11-01

    The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

  7. GAUSS Project Trials Results

    NASA Astrophysics Data System (ADS)

    Di Fazio, Antonella; Vernucci, Antonio; Rossini, Eugenio

    2003-07-01

    GAUSS is a Research and Technological Development project co-funded by European Commission, within the frame of the IST (Information Society Technologies) V Programme. It is a two-year project, starting from December 2000, and successfully completed.The GAUSS Team involves a Consortium of nine European companies, including ARNI (Azienda Regionale per la Navigazione Interna, I), ASCOM (CH), ERICSSON Telecomunicazioni (I), GMV (E), TELEFONICA (E), THALES Navigation (F), TTI Norte (E), Space Engineering (I) and TELESPAZIO (I) as project co-ordinator.GAUSS objective was to design and demonstrate the feasibility of a system providing Location-based services, from the integration of Satellite Navigation and Communications, within the contexts of GALILEO and the UMTS technology. The GAUSS proposed solution supports highly reliable, near real-time two-way communication between Mobile Users and Service Centre/Provider. The services considered for GAUSS are based on exchange at low data rate transmission of small data packets carrying very accurate positioning & timing information, as typically required by Info-Mobility and Inter-Modality oriented applications. These services are characterised by bursty and unbalanced traffic, generated by a large number of Mobile Users towards a relatively small number of Service Providers, and viceversa from the Service Providers towards widely geographically sparse Mobile Users (i.e. greater amount of traffic in the return link with respect to the forward link). The GAUSS system supports both asynchronous and synchronous communication, based on: ß broad-casting (i.e. data distribution from a Service Provider to Mobile Users)ß broad-catching (i.e. data collection from MUs to a SP)ß point-to-point schemes.Resource access is based on CDMA (Code Division Multiple Access), according to the UMTS standard. A Demonstrator was built up by combining existing facilities with innovative hardware and software components, ad-hoc developed by some of the Consortium Partners. The former ones constitute the ground and space segments, the latter ones include the advanced user terminal and the applications. The assembled system was used as test-bed during the trail campaign, to validate and prove the provided services and developed applications.The GAUSS Demonstrator includes the following components:ß The Mobile User Terminal installed on a car (van) or on a boat. An innovative multi-mode user equipment was developed, consisting of the following main components:- An integrated NAV / COM digital receive front-end (DFRE), able to de-multiplex the NAV signals (the current GNSS1 band and the simulated Galileo bands), and the COM signal in the S-UMTS band;- For COM: a transmit front-end, and a baseband & control section operating in CDMA and supporting the upper protocol layers (UMTS packet transmission standard based - for short packet); a RF subsystem, including the L→S bands conversion;- For NAV: a GNSS (GPS, EGNOS) navigation receiver, the GNSS1 System (MTB - Mediterranean Test bed, ESTB / EGNOS System Test Bed) for navigation;* The Communication capacity on the INMARSAT 3F5 Satellite* The Gateway, located in LARIO Telespazio premises* The Lario07 Station* The Service Centre* The Service Provider.The GAUSS Demonstrator reflects all the main elements of a complete user platform for service provisioning: mobility assistance, safety and transport efficient management are the core of the developed applications. Applications were developed, specifically to provide reliable and effective services to the citizens: road info-mobility and fleet management, inland waterways vessel traffic management and information, port/terminals appointment monitoring & control, dangerous goods transhipment supervision, emergency assistance.A trial campaign, run into real environments, was performed in Summer 2002. GAUSS Demonstrator performances and benefits were validated with the direct involvement of an inter-modal transport user, specifically operating in inland- waterways and roads. Safety-of-life applications for assisted vessel navigation and for management of hazardous goods (gas) transhipment over the Po river were thoroughly tested and assessed. Applications for emergency assistance, Point of Interest inquiry, localisation of commercial fleet were also proven.GAUSS successfully demonstrated integrated GNSS1 precise positioning based on EGNOS and satellite UMTS packet communication. The new technology with respect to the current state-of the art, developed within the project, was validated during the trial campaign, including the implemented broadcasting and multicasting communication of data packet compliant to 3GPP standard (current release 4). Horizontal accuracy better than 3-m was achieved in the trial area (Northern Italy - Lario - Como Lake, Parma and Po river areas), thanks to the navigation functions based on GPS signals augmented with SBAS techniques. The MTB (Mediterranean Test Bed) was utilised because of the poor performance coverage of the ESTB system over the Italian regions.In this paper, the results of the GAUSS trial campaign are reported, along with their assessment and evaluation in terms of possible enhancements and future exploitations.

  8. On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

    PubMed

    Dadhich, Naresh; Pons, Josep M

    We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.

  9. Integrated metagenomic analysis of the rumen microbiome of cattle reveals key biological mechanisms associated with methane traits.

    PubMed

    Wang, Haiying; Zheng, Huiru; Browne, Fiona; Roehe, Rainer; Dewhurst, Richard J; Engel, Felix; Hemmje, Matthias; Lu, Xiangwu; Walsh, Paul

    2017-07-15

    Methane is one of the major contributors to global warming. The rumen microbiota is directly involved in methane production in cattle. The link between variation in rumen microbial communities and host genetics has important applications and implications in bioscience. Having the potential to reveal the full extent of microbial gene diversity and complex microbial interactions, integrated metagenomics and network analysis holds great promise in this endeavour. This study investigates the rumen microbial community in cattle through the integration of metagenomic and network-based approaches. Based on the relative abundance of 1570 microbial genes identified in a metagenomics analysis, the co-abundance network was constructed and functional modules of microbial genes were identified. One of the main contributions is to develop a random matrix theory-based approach to automatically determining the correlation threshold used to construct the co-abundance network. The resulting network, consisting of 549 microbial genes and 3349 connections, exhibits a clear modular structure with certain trait-specific genes highly over-represented in modules. More specifically, all the 20 genes previously identified to be associated with methane emissions are found in a module (hypergeometric test, p<10 -11 ). One third of genes are involved in methane metabolism pathways. The further examination of abundance profiles across 8 samples of genes highlights that the revealed pattern of metagenomics abundance has a strong association with methane emissions. Furthermore, the module is significantly enriched with microbial genes encoding enzymes that are directly involved in methanogenesis (hypergeometric test, p<10 -9 ). Copyright © 2017 Elsevier Inc. All rights reserved.

  10. Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

    2017-07-01

    We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

  11. Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

    PubMed Central

    Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

    2018-01-01

    The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning (“PDR”). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model (“GMM”), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model (“GHM”). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation. PMID:29385076

  12. Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors.

    PubMed

    Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

    2018-01-31

    The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning ("PDR"). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model ("GMM"), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model ("GHM"). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

  13. Performance Benchmark for a Prismatic Flow Solver

    DTIC Science & Technology

    2007-03-26

    Gauss- Seidel (LU-SGS) implicit method is used for time integration to reduce the computational time. A one-equation turbulence model by Goldberg and...numerical flux computations. The Lower-Upper-Symmetric Gauss- Seidel (LU-SGS) implicit method [1] is used for time integration to reduce the...Sharov, D. and Nakahashi, K., “Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss- Seidel Computations,” AIAA Journal, Vol. 36

  14. The AGS Ggamma Meter and Calibrating the Gauss Clock

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ahrens, Leif

    2014-03-31

    During AGS Polarized Proton acceleration periods, one output from the AGS Ggamma Meter, namely the energy (or Ggamma) calculated from the magnetic field in the AGS main magnets and the beam radius- both measured in particular instant, is used to figure out the times in the AGS magnet acceleration cycle when the beam passes through a particular set of depolarizing resonances. The resonance set occur whenever a particle’s Ggamma (energy*(G/m) becomes nearly equal to n*Qx (i.e. any integer multiplied by the horizontal betatron tune). This deliverable is why the machinery is referred to as the ''Ggamma Meter'' rather than themore » AGS energy meter. The Ggamma Meter takes as inputs a set of measurements of frequency (F(t)), radius (r(t)), and gauss clock counts (GCC(t)). The other energy (GgammaBr) assumes the field when the gauss clock starts counting is known. The change in field to time t is given by the measured accumulated gauss clock counts multiplied by the gauss clock calibration (gauss/GCC). In order to deal with experimental data, this calibration factor gets an added ad hoc complication, namely a correction dependent on the rate of change the counting rate. The Ggamma meter takes GCC(t) and together with the past history for this cycle calculates B(t).« less

  15. Three-point functions in duality-invariant higher-derivative gravity

    DOE PAGES

    Naseer, Usman; Zwiebach, Barton

    2016-03-21

    Here, doubled α'-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in α'. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in α'.

  16. The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions

    NASA Astrophysics Data System (ADS)

    Górska, K.; Horzela, A.; Bratek, Ł.; Dattoli, G.; Penson, K. A.

    2018-04-01

    We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern proportional in the frequency domain to [1+(iωτ0){\\hspace{0pt}}α]-β with τ0 > 0 being some characteristic time. For α = l/k< 1 (l and k being positive and relatively prime integers) and β > 0 we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their domain dual in the sense of the inverse Laplace transform. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization β = (2-q)/(q-1) and τ0 = (q-1){\\hspace{0pt}}1/α (1 < q < 2) we show that for 0 < α < 1 the response functions fα, β(t/τ0) go to the one-sided Lévy stable distributions when q tends to one. Moreover, applying the self-similarity property of the probability densities gα, β(u) , we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.

  17. A Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

    NASA Astrophysics Data System (ADS)

    Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

    2017-12-01

    This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

  18. Bearings Only Tracking with Fusion from Heterogenous Passive Sensors: ESM/EO and Acoustic

    DTIC Science & Technology

    2017-02-01

    consists of an unscented Kalman filter (UKF) to handle in-sequence ESM/EO measurements and an OOSM unscented Gauss-Helmert filter (OOSM-UGHF) to handle out...bearings-only tracking, target motion analysis, unscented Gauss-Helmert filter , out-of-sequence measurement. I. INTRODUCTION The commonly used passive...proposed an unscented Gauss-Helmert filter (UGHF) [22] [21] to solve this problem. The existing UGHF works with in-sequence measurements. Further

  19. On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations

    NASA Technical Reports Server (NTRS)

    Tsao, Nai-Kuan

    1989-01-01

    A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.

  20. Gauss Seidel-type methods for energy states of a multi-component Bose Einstein condensate

    NASA Astrophysics Data System (ADS)

    Chang, Shu-Ming; Lin, Wen-Wei; Shieh, Shih-Feng

    2005-01-01

    In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigenvalue problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

  1. Mode coupling in vortex beams

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil T.

    2018-05-01

    We examine the mode coupling in vortex beams. Mode coupling also known as the crosstalk takes place due to turbulent characteristics of the atmospheric communication medium. This way, the transmitted intrinsic mode of the vortex beam leaks power to other extrinsic modes, thus preventing the correct detection of the transmitted symbol which is usually encoded into the mode index or the orbital angular momentum state of the vortex beam. Here we investigate the normalized power mode coupling ratios of several types of vortex beams, namely, Gaussian vortex beam, Bessel Gaussian beam, hypergeometric Gaussian beam and Laguerre Gaussian beam. It is found that smaller mode numbers lead to less mode coupling. The same is partially observed for increasing source sizes. Comparing the vortex beams amongst themselves, it is seen that hypergeometric Gaussian beam is the one retaining the most power in intrinsic mode during propagation, but only at lowest mode index of unity. At higher mode indices this advantage passes over to the Gaussian vortex beam.

  2. Variational Dirac-Hartree-Fock calculation of the Breit interaction

    NASA Astrophysics Data System (ADS)

    Goldman, S. P.

    1988-04-01

    The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

  3. Solution to urn models of pairwise interaction with application to social, physical, and biological sciences

    NASA Astrophysics Data System (ADS)

    Pickering, William; Lim, Chjan

    2017-07-01

    We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms.

  4. Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

    NASA Astrophysics Data System (ADS)

    Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

    2018-04-01

    We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

  5. A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

    DTIC Science & Technology

    2013-02-01

    obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

  6. GAUSS Market Analysis for Integrated Satellite Communication and Navigation Location Based services

    NASA Astrophysics Data System (ADS)

    Di Fazio, Antonella; Dricot, Fabienne; Tata, Francesco

    2003-07-01

    The demand for mobile information services coupled with positioning technologies for delivering value- added services that depend on a user's location has rapidly increased during last years. In particular, services and applications related with improved mobility safety and transport efficiency look very attractive.Solutions for location services vary in respect of positioning accuracy and the technical infrastructure required, and the associated investment in terminals and networks. From the analysis of the state-of-the art, it comes that various technologies are currently available on the European market, while mobile industry is gearing up to launch a wide variety of location services like tracking, alarming and locating.Nevertheless, when addressing safety of life as well as security applications, severe hurdles have to be posed in the light of existing technologies. Existing navigation (e.g. GPS) and communication systems are not able to completely satisfy the needs and requirements of safety-of-life-critical applications. As a matter of fact, the GPS system's main weaknesses today is its lack of integrity, which means its inability to warn users of a malfunction in a reasonable time, while the other positioning techniques do not provide satisfactory accuracy as well, and terrestrial communication networks are not capable to cope with stringent requirement in terms of service reliability and coverage.In this context, GAUSS proposes an innovative satellite-based solution using novel technology and effective tools for addressing mobility challenges in a cost efficient manner, improving safety and effectiveness.GAUSS (Galileo And UMTS Synergetic System) is a Research and Technological Development project co- funded by European Commission, within the frame of the 5th IST Programme. The project lasted two years, and it was successfully completed in November 2002. GAUSS key concept is the integration of Satellite Navigation GNSS and UMTS communication technology, to provide high quality location based services (tracking, tracing, alarming, messaging, group broadcasting, fleet management information) oriented to mass and business markets transport & mobility management. The GAUSS rationales for the proposed solution rely on the consideration that the existing and available systems are not capable to completely fulfil stringent requirements for the navigation and communication capabilities, in terms of integrity/continuity positioning and guarantee of performances, as those coming from classes of users in the inter-modality and specific personal info-mobility sectors.For the navigation functions, the use of GALILEO will ensure a guaranteed quality of service and adequate performances, in terms of accuracy and integrity, as required for safety and working condition improvements (such as restricted waterways - ports, coasts, rivers - and hazardous goods transportation). Furthermore, it also will enable to cope with liability and certification requirements that are needed for responsibility issues, in case of damages or accidents.From the communication viewpoint, the challenges reside on the usage of the UMTS. This enables to fit GAUSS into an open market place: avoiding proliferation of standards and adoption of open interfaces to be defined by the business interest. Furthermore, the GAUSS solution fully exploits the advantages coming from the usage of the satellite of offering solutions for effectively complement terrestrial based systems (fast and large coverage, economically viable set-up cost, efficient provisioning of broadcasting and multicasting features, gap filler capability).A comprehensive market analysis was carried out in the frame of the project, aimed at investigating the techno-economical viability for a possible commercial introduction of the proposed solution.This paper presents the output of the performed studies, resulting in a realistic picture of the GAUSS market:§ Identification of potential actors/players (operators, manufacturers, professional and mass market users, service providers, authorities, etc.)§ Competitive analysis§ Market size and segmentation, and GAUSS position in the market§ Business models§ Business plan and cost/benefit ratio§ Identification of market opportunities for services and applications, in view of the future GALILEO and S-UMTS.

  7. Distributions in Spherical Coordinates with Applications to Classical Electrodynamics

    ERIC Educational Resources Information Center

    Gsponer, Andre

    2007-01-01

    A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that all delta functions and their derivatives are automatically generated, and ensures that the Gauss theorem is…

  8. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

    PubMed

    Frisvad, Jeppe Revall

    2018-04-01

    In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

  9. Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

    NASA Astrophysics Data System (ADS)

    Bervillier, C.; Boisseau, B.; Giacomini, H.

    2008-02-01

    The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

  10. Coagulation-fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus

    NASA Astrophysics Data System (ADS)

    Hozé, Nathanaël; Holcman, David

    2012-01-01

    We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.

  11. Gauss-Bonnet chameleon mechanism of dark energy

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ito, Yusaku; Nojiri, Shin'ichi

    2009-05-15

    As a model of the current accelerated expansion of the Universe, we consider a model of the scalar-Einstein-Gauss-Bonnet gravity. This model includes the propagating scalar modes, which might give a large correction to the Newton law. In order to avoid this problem, we propose an extension of the chameleon mechanism where the scalar mode becomes massive due to the coupling with the Gauss-Bonnet term. Since the Gauss-Bonnet invariant does not vanish near the Earth or in the Solar System, even in the vacuum, the scalar mode is massive even in the vacuum and the correction to the Newton law couldmore » be small. We also discuss the possibility that the model could describe simultaneously the inflation in the early Universe, in addition to the current accelerated expansion.« less

  12. Apparatus and method for enhancing tissue repair in mammals

    NASA Technical Reports Server (NTRS)

    Goodwin, Thomas J. (Inventor); Parker, Clayton R. (Inventor)

    2009-01-01

    An apparatus is introduced for the use of enhancing tissue repair in mammals. The apparatus includes a sleeve; an electrically conductive coil; a sleeve support; an electrical circuit configured to supply the coil with a square wave time varying electrical current sufficient to create approximately 0.05 gauss to 0.5 gauss. When in use, the sleeve of the apparatus is placed on a mammalian body part and the time varying electromagnetic force of from approximately 0.05 gauss to 0.5 gauss is generated on the mammalian body for an extended period of time so that the tissue is encouraged to be regenerated in the mammalian body part at a rate in excess of the normal tissue regeneration rate relative to regeneration without application of the time varying electromagnetic force.

  13. Fuchsian triangle groups and Grothendieck dessins. Variations on a theme of Belyi

    NASA Astrophysics Data System (ADS)

    Cohen, Paula Beazley; Itzykson, Claude; Wolfart, Jürgen

    1994-07-01

    According to a theorem of Belyi, a smooth projective algebraic curve is defined over a number field if and only if there exists a non-constant element of its function field ramified only over 0, 1 and . The existence of such a Belyi function is equivalent to that of a representation of the curve as a possibly compactified quotient space of the Poincaré upper half plane by a subgroup of finite index in a Fuchsian triangle group. On the other hand, Fuchsian triangle groups arise in many contexts, such as in the theory of hypergeometric functions and certain triangular billiard problems, which would appear at first sight to have no relation to the Galois problems that motivated the above discovery of Belyi. In this note we review several results related to Belyi's theorem and we develop certain aspects giving examples. For preliminary accounts, see the preprint [Wo1], the conference proceedings article [BauItz] and the Comptes Rendus note [CoWo2].

  14. Circadian Rhythms in Plants, Insects and Mammals Exposed to ELF Magnetic and/or Electric Fields and Currents

    DTIC Science & Technology

    1975-08-28

    favorable to the model. Parameter estimates from this fitting process, carried out in the nature of a "moving-average" throughout the cntilre serces of...34OWOLS Pl %%t4)1 uSSvMS~ USA NIWW 162-7-020 r,.6/WEfg 4/R:0 GAUSS.8:O.5 GAUSS.C:I.O GAUSS.D:2.0 GAtJ$ 360 :24 i ONCHRNHEC SCHOUL if .) 75.2 40.0 20

  15. Large Deviations and Quasipotential for Finite State Mean Field Interacting Particle Systems

    DTIC Science & Technology

    2014-05-01

    The conclusion then follows by applying Lemma 4.4.2. 132 119 4.4.1 Iterative solver: The widest neighborhood structure We employ Gauss - Seidel ...nearest neighborhood structure described in Section 4.4.2. We use Gauss - Seidel iterative method for our numerical experiments. The Gauss - Seidel ...x ∈ Bh, M x ∈ Sh\\Bh, where M ∈ (V,∞) is a very large number, so that the iteration (4.5.1) converges quickly. For simplicity, we restrict our

  16. A Fast and Accurate Algorithm for l1 Minimization Problems in Compressive Sampling (Preprint)

    DTIC Science & Technology

    2013-01-22

    However, updating uk+1 via the formulation of Step 2 in Algorithm 1 can be implemented through the use of the component-wise Gauss - Seidel iteration which...may accelerate the rate of convergence of the algorithm and therefore reduce the total CPU-time consumed. The efficiency of component-wise Gauss - Seidel ...Micchelli, L. Shen, and Y. Xu, A proximity algorithm accelerated by Gauss - Seidel iterations for L1/TV denoising models, Inverse Problems, 28 (2012), p

  17. Generalizations of the Alternating Direction Method of Multipliers for Large-Scale and Distributed Optimization

    DTIC Science & Technology

    2014-05-01

    exact one is solved later — as- signed as step 5 of Algorithm 2 — because at each iteration , the ADMM updates the variables in the Gauss - Seidel ...Jacobi ADMM (see Algo- rithm 5 below). Unlike the Gauss - Seidel ADMM, the Jacobi ADMM updates all the 70 blocks in parallel at every iteration : xk+1i...that extending ADMM straightforwardly from the classic Gauss - Seidel setting to the Jacobi setting, from two blocks to multiple blocks, will preserve

  18. Addendum to ''Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity''

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Simeone, Claudio

    2011-04-15

    Thin-shell wormholes are constructed starting from the exotic branch of the Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations supported by matter satisfying the energy conditions exist for certain values of the parameters. Differing from the previous result associated with the normal branch of the Wiltshire solution, this is achieved for small positive values of the Gauss-Bonnet parameter and for vanishing charge.

  19. Optimal Keno Strategies and the Central Limit Theorem

    ERIC Educational Resources Information Center

    Johnson, Roger W.

    2006-01-01

    For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

  20. Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

    NASA Astrophysics Data System (ADS)

    Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

    2018-05-01

    We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

  1. Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling

    NASA Astrophysics Data System (ADS)

    Chakrabarti, Soumya

    2018-04-01

    We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with the Gauss-Bonnet term, a self-interaction potential and an additional perfect fluid distribution alongwith the scalar field, we investigate different possibilities regarding the outcome of the collapsing scalar field. The strength of the coupling and choice of the self-interaction potential serves as the pivotal initial conditions of the models presented. The high degree of non-linearity in the equation system is taken care off by using a method of invertibe point transformation of anharmonic oscillator equation, which has proven itself very useful in recent past while investigating dynamics of minimally coupled scalar fields.

  2. Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

    2014-03-01

    A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

  3. Composite Gauss-Legendre Quadrature with Error Control

    ERIC Educational Resources Information Center

    Prentice, J. S. C.

    2011-01-01

    We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)

  4. Basis set construction for molecular electronic structure theory: natural orbital and Gauss-Slater basis for smooth pseudopotentials.

    PubMed

    Petruzielo, F R; Toulouse, Julien; Umrigar, C J

    2011-02-14

    A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.

  5. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gorbachev, D V; Ivanov, V I

    Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

  6. Proceedings of the Fourth Annual U.S. Army Conference on Applied Statistics, 21-23 October 1998.

    DTIC Science & Technology

    1999-11-01

    1833) published a memoir Nouvelles mithodes pour la determination des cometes in which he introduced and named the method of least squares. In 1809...251,1972. 2. Sprott, D. A. "Gauss’s Contributions to Statistics." Historia Mathematica, vol. 5, pp. 183-203,1978. 3. Stigler, S. M. "An Attack on Gauss...Published by Legendre in 1820." Historia Mathematica. vol. 4, pp. 31-35, 1977. 4. Stigler, S. M. "Gauss and the Invention of Least Squares." The

  7. The magnetic field of saturn: pioneer 11 observations.

    PubMed

    Acuña, M H; Ness, N F

    1980-01-25

    The intrinsic magnetic field of Saturn measured by the high-field fluxgate magnetometer is much weaker than expected. An analysis of preliminary data combined with the preliminary trajectory yield a model for the main planetary field which is a simple centered dipole of moment 0.20 +/- 0.01 gauss-Rs(3) = 4.3 +/- 0.2 x 10(28) gauss-cm(3) (1 Rs = 1 Saturn radius = 60,000 km). The polarity is opposite that of Earth, and, surprisingly, the tilt is small, within 2 degrees +/- 1 degrees of the rotation axis. The equatorial field intensity at the cloud tops is 0.2 gauss, and the polar intensity is 0.56 gauss. The unique moon Titan is expected to be located within the magnetosheath of Saturn or the interplanetary medium about 50 percent of the time because the average subsolar point distance to the magnetosphere is estimated to be 20 Rs, the orbital distance to Titan.

  8. Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dotti, Gustavo; Instituto de Fisica Enrique Gaviola, CONICET, Cordoba; Oliva, Julio

    2010-07-15

    The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d{>=}5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximallymore » symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.« less

  9. On the parametrization of lateral dose profiles in proton radiation therapy.

    PubMed

    Bellinzona, V E; Ciocca, M; Embriaco, A; Fontana, A; Mairani, A; Mori, M; Parodi, K

    2015-07-01

    The accurate evaluation of the lateral dose profile is an important issue in the field of proton radiation therapy. The beam spread, due to Multiple Coulomb Scattering (MCS), is described by the Molière's theory. To take into account also the contribution of nuclear interactions, modern Treatment Planning Systems (TPSs) generally approximate the dose profiles by a sum of Gaussian functions. In this paper we have compared different parametrizations for the lateral dose profile of protons in water for therapeutical energies: the goal is to improve the performances of the actual treatment planning. We have simulated typical dose profiles at the CNAO (Centro Nazionale di Adroterapia Oncologica) beamline with the FLUKA code and validated them with data taken at CNAO considering different energies and depths. We then performed best fits of the lateral dose profiles for different functions using ROOT and MINUIT. The accuracy of the best fits was analyzed by evaluating the reduced χ(2), the number of free parameters of the functions and the calculation time. The best results were obtained with the triple Gaussian and double Gaussian Lorentz-Cauchy functions which have 6 parameters, but good results were also obtained with the so called Gauss-Rutherford function which has only 4 parameters. The comparison of the studied functions with accurate and validated Monte Carlo calculations and with experimental data from CNAO lead us to propose an original parametrization, the Gauss-Rutherford function, to describe the lateral dose profiles of proton beams. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

  10. A magnetic-piezoelectric smart material-structure sensing three axis DC and AC magnetic-fields

    NASA Astrophysics Data System (ADS)

    Hung, Chiao-Fang; Chen, Chin-Chung; Yeh, Po-Chen; Chen, Po-Wen; Chung, Tien-Kan

    2017-12-01

    In this paper, we demonstrate a smart material-structure can sense not only three-axis AC magnetic-fields but also three-axis DC magnetic-fields. Under x-axis and z-axis AC magnetic field ranging from 0.2 to 3.2 gauss, sensing sensitivity of the smart material-structure stimulated at resonant frequency is approximate 8.79 and 2.80 mV/gauss, respectively. In addition, under x-axis and z-axis DC magnetic fields ranging from 2 to 12 gauss, the sensitivity of the smart material-structure is 1.24-1.54 and 1.25-1.41 mV/gauss, respectively. In addition, under x-axis and z-axis DC magnetic fields ranging from 12 to 20 gauss, the sensitivity of the smart material-structure is 5.17-6.2 and 3.97-4.57 mV/gauss, respectively. These experimental results show that the smart material-structure successfully achieves three-axis DC and AC magnetic sensing as we designed. Furthermore, we also compare the results of the AC and DC magnetic-field sensing to investigate discrepancies. Finally, when applying composite magnetic-fields to the smart material-structure, the smart material-structure shows decent outputs as expected (consistent to the sensing principle). In the future, we believe the smart material-structure capable of sensing AC and DC magnetic fields will have more applications than conventional structures capable of sensing only DC or AC magnetic field. Thus, the smart material-structure will be an important design reference for future magnetic-field sensing technologies.

  11. A Guided Tour of Mathematical Methods

    NASA Astrophysics Data System (ADS)

    Snieder, Roel

    2009-04-01

    1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

  12. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ahmed, Jawad; Shahzad, Azeem; Khan, Masood

    This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differentialmore » equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.« less

  13. Quadrature, Interpolation and Observability

    NASA Technical Reports Server (NTRS)

    Hodges, Lucille McDaniel

    1997-01-01

    Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.

  14. Impacts of Sigma Coordinates on the Euler and Navier-Stokes Equations using Continuous Galerkin Methods

    DTIC Science & Technology

    2009-03-01

    the 1- D local basis functions. The 1-D Lagrange polynomial local basis function, using Legendre -Gauss-Lobatto interpolation points, was defined by...cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K with an interval of 0.025 K...after 700 s for reso- lutions: (a) 20, (b) 10, and (c) 5 m. All cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K

  15. Advances in Highly Constrained Multi-Phase Trajectory Generation using the General Pseudospectral Optimization Software (GPOPS)

    DTIC Science & Technology

    2013-08-01

    release; distribution unlimited. PA Number 412-TW-PA-13395 f generic function g acceleration due to gravity h altitude L aerodynamic lift force L Lagrange...cost m vehicle mass M Mach number n number of coefficients in polynomial regression p highest order of polynomial regression Q dynamic pressure R...Method (RPM); the collocation points are defined by the roots of Legendre -Gauss- Radau (LGR) functions.9 GPOPS also automatically refines the “mesh” by

  16. Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

    NASA Astrophysics Data System (ADS)

    Li, Xiao; Scaglione, Anna

    2013-11-01

    The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

  17. Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave.

    PubMed

    Lin, Jiao; Dellinger, Jean; Genevet, Patrice; Cluzel, Benoit; de Fornel, Frederique; Capasso, Federico

    2012-08-31

    A new surface wave is introduced, the cosine-Gauss beam, which does not diffract while it propagates in a straight line and tightly bound to the metallic surface for distances up to 80 μm. The generation of this highly localized wave is shown to be straightforward and highly controllable, with varying degrees of transverse confinement and directionality, by fabricating a plasmon launcher consisting of intersecting metallic gratings. Cosine-Gauss beams have potential for applications in plasmonics, notably for efficient coupling to nanophotonic devices, opening up new design possibilities for next-generation optical interconnects.

  18. Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

    NASA Astrophysics Data System (ADS)

    Samohyl, Robert Wayne

    2017-10-01

    This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The article presents R code throughout.

  19. Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values

    NASA Astrophysics Data System (ADS)

    Van Assche, W.; Yáñez, R. J.; González-Férez, R.; Dehesa, Jesús S.

    2000-09-01

    The system of Gegenbauer or ultraspherical polynomials {Cnλ(x);n=0,1,…} is a classical family of polynomials orthogonal with respect to the weight function ωλ(x)=(1-x2)λ-1/2 on the support interval [-1,+1]. Integral functionals of Gegenbauer polynomials with integrand f(x)[Cnλ(x)]2ωλ(x), where f(x) is an arbitrary function which does not depend on n or λ, are considered in this paper. First, a general recursion formula for these functionals is obtained. Then, the explicit expression for some specific functionals of this type is found in a closed and compact form; namely, for the functionals with f(x) equal to (1-x)α(1+x)β, log(1-x2), and (1+x)log(1+x), which appear in numerous physico-mathematical problems. Finally, these functionals are used in the explicit evaluation of the momentum expectation values and of the D-dimensional hydrogenic atom with nuclear charge Z⩾1. The power expectation values are given by means of a terminating 5F4 hypergeometric function with unit argument, which is a considerable improvement with respect to Hey's expression (the only one existing up to now) which requires a double sum.

  20. Generating functions for weighted Hurwitz numbers

    NASA Astrophysics Data System (ADS)

    Guay-Paquet, Mathieu; Harnad, J.

    2017-08-01

    Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ -functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as a weight generator, three new types of weighted enumerations are introduced. These determine quantum Hurwitz numbers depending on a deformation parameter q. By suitable interpretation of q, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.

  1. Analytic properties for the honeycomb lattice Green function at the origin

    NASA Astrophysics Data System (ADS)

    Joyce, G. S.

    2018-05-01

    The analytic properties of the honeycomb lattice Green function are investigated, where is a complex variable which lies in a plane. This double integral defines a single-valued analytic function provided that a cut is made along the real axis from w  =  ‑3 to . In order to analyse the behaviour of along the edges of the cut it is convenient to define the limit function where . It is shown that and can be evaluated exactly for all in terms of various hypergeometric functions, where the argument function is always real-valued and rational. The second-order linear Fuchsian differential equation satisfied by is also used to derive series expansions for and which are valid in the neighbourhood of the regular singular points and . Integral representations are established for and , where with . In particular, it is proved that where J 0(z) and Y 0(z) denote Bessel functions of the first and second kind, respectively. The results derived in the paper are utilized to evaluate the associated logarithmic integral where w lies in the cut plane. A new set of orthogonal polynomials which are connected with the honeycomb lattice Green function are also briefly discussed. Finally, a link between and the theory of Pearson random walks in a plane is established.

  2. Propagation dynamics of Helical Hermite-Gaussian beams

    NASA Astrophysics Data System (ADS)

    López-Mariscal, Carlos; Gutiérrez-Vega, Julio C.

    2007-09-01

    We investigate theoretically and experimentally the propagation characteristics of the Helical Hermite-Gauss beams corresponding to the helical Ince-Gauss beams in the limit of infinite ellipticity. Particular attention is paid to the transverse irradiance structure, the orbital angular momentum density, and the vortex distribution.

  3. Wake Numerical Simulation Based on the Park-Gauss Model and Considering Atmospheric Stability

    NASA Astrophysics Data System (ADS)

    Yang, Xiangsheng; Zhao, Ning; Tian, Linlin; Zhu, Jun

    2016-06-01

    In this paper, a new Park-Gauss model based on the assumption of the Park model and the Eddy-viscosity model is investigated to conduct the wake numerical simulation for solving a single wind turbine problem. The initial wake radius has been modified to improve the model’s numerical accuracy. Then the impact of the atmospheric stability based on the Park-Gauss model has been studied in the wake region. By the comparisons and the analyses of the test results, it turns out that the new Park-Gauss model could achieve better effects of the wind velocity simulation in the wake region. The wind velocity in the wake region recovers quickly under the unstable atmospheric condition provided the wind velocity is closest to the test result, and recovers slowly under stable atmospheric condition in case of the wind velocity is lower than the test result. Meanwhile, the wind velocity recovery falls in between the unstable and stable neutral atmospheric conditions.

  4. Steady state numerical solutions for determining the location of MEMS on projectile

    NASA Astrophysics Data System (ADS)

    Abiprayu, K.; Abdigusna, M. F. F.; Gunawan, P. H.

    2018-03-01

    This paper is devoted to compare the numerical solutions for the steady and unsteady state heat distribution model on projectile. Here, the best location for installing of the MEMS on the projectile based on the surface temperature is investigated. Numerical iteration methods, Jacobi and Gauss-Seidel have been elaborated to solve the steady state heat distribution model on projectile. The results using Jacobi and Gauss-Seidel are shown identical but the discrepancy iteration cost for each methods is gained. Using Jacobi’s method, the iteration cost is 350 iterations. Meanwhile, using Gauss-Seidel 188 iterations are obtained, faster than the Jacobi’s method. The comparison of the simulation by steady state model and the unsteady state model by a reference is shown satisfying. Moreover, the best candidate for installing MEMS on projectile is observed at pointT(10, 0) which has the lowest temperature for the other points. The temperature using Jacobi and Gauss-Seidel for scenario 1 and 2 atT(10, 0) are 307 and 309 Kelvin respectively.

  5. Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers

    NASA Astrophysics Data System (ADS)

    Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen

    2017-06-01

    The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.

  6. Cosmology of a holographic induced gravity model with curvature effects

    NASA Astrophysics Data System (ADS)

    Bouhmadi-López, Mariam; Errahmani, Ahmed; Ouali, Taoufiq

    2011-10-01

    We present a holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalizes the normal Dvali-Gabadadze-Porrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and a holographic dark energy with the Hubble scale as the infrared cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal Dvali-Gabadadze-Porrati branch (without Gauss-Bonnet modifications) nor in a standard four-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.

  7. Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.; Helenbrook, B. T.

    2005-01-01

    This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

  8. Apparatus for enhancing tissue repair in mammals

    NASA Technical Reports Server (NTRS)

    Goodwin, Thomas J. (Inventor); Parker, Clayton R. (Inventor)

    2007-01-01

    An apparatus is disclosed for enhancing tissue repair in mammals, with the apparatus comprising: a sleeve for encircling a portion of a mammalian body part, said sleeve comprising an electrically conductive coil capable of generating an electromagnetic field when an electrical current is applied thereto, means for supporting the sleeve on the mammalian body part; and means for supplying the electrically conductive coil with a square wave time varying electrical current sufficient to create a time varying electromagnetic force of from approximately 0.05 gauss to 0.05 gauss within the interior of the coil in order that when the sleeve is placed on a mammalian body part and the time varying electromagnetic force of from approximately 0.05 gauss to 0.05 gauss is generated on the mammalian body part for an extended period of time, tissue regeneration within the mammalian body part is increased to a rate in excess of the normal tissue regeneration rate that would occur without application of the time varying electromagnetic force.

  9. Systems Biology Approaches for Discovering Biomarkers for Traumatic Brain Injury

    DTIC Science & Technology

    2013-07-01

    injury (FPI), in which injury is produced by the impact of a pendulum onto a fluid reservoir, or controlled cortical impact (CCI), in which a rigid...algorithm, and the MSigDB Web site in Table 3 allows users to run GSEA on up- loaded data. One drawback to GSEA and the hypergeometric test is that

  10. Exact axially symmetric galactic dynamos

    NASA Astrophysics Data System (ADS)

    Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.

    2018-05-01

    We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.

  11. A memory efficient implementation scheme of Gauss error function in a Laguerre-Volterra network for neuroprosthetic devices

    NASA Astrophysics Data System (ADS)

    Li, Will X. Y.; Cui, Ke; Zhang, Wei

    2017-04-01

    Cognitive neural prosthesis is a manmade device which can be used to restore or compensate for lost human cognitive modalities. The generalized Laguerre-Volterra (GLV) network serves as a robust mathematical underpinning for the development of such prosthetic instrument. In this paper, a hardware implementation scheme of Gauss error function for the GLV network targeting reconfigurable platforms is reported. Numerical approximations are formulated which transform the computation of nonelementary function into combinational operations of elementary functions, and memory-intensive look-up table (LUT) based approaches can therefore be circumvented. The computational precision can be made adjustable with the utilization of an error compensation scheme, which is proposed based on the experimental observation of the mathematical characteristics of the error trajectory. The precision can be further customizable by exploiting the run-time characteristics of the reconfigurable system. Compared to the polynomial expansion based implementation scheme, the utilization of slice LUTs, occupied slices, and DSP48E1s on a Xilinx XC6VLX240T field-programmable gate array has decreased by 94.2%, 94.1%, and 90.0%, respectively. While compared to the look-up table based scheme, 1.0 ×1017 bits of storage can be spared under the maximum allowable error of 1.0 ×10-3 . The proposed implementation scheme can be employed in the study of large-scale neural ensemble activity and in the design and development of neural prosthetic device.

  12. Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.

    PubMed

    Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen

    2011-04-15

    We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.

  13. Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals

    NASA Astrophysics Data System (ADS)

    Pastras, Georgios; Manolopoulos, Dimitrios

    2014-11-01

    We calculate the Rényi entropy S q ( μ, λ), for spherical entangling surfaces in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ, larger than specific value, but still allowed by causality, we observe a violation of the inequality , which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q ( μ, λ) for imaginary chemical potential, between negative and non-negative λ.

  14. The crypto-Hermitian smeared-coordinate representation of wave functions

    NASA Astrophysics Data System (ADS)

    Znojil, Miloslav

    2011-08-01

    In discrete-coordinate quantum models the kinematical observable of position need not necessarily be chosen local (i.e., diagonal). Its smearing is selected in the nearest-neighbor form of a real asymmetric (i.e., crypto-Hermitian) tridiagonal matrix Qˆ. Via Gauss-Hermite illustrative example we show how such an option restricts the class of admissible dynamical observables (sampled here just by the Hamiltonian).

  15. High-accuracy 3D Fourier forward modeling of gravity field based on the Gauss-FFT technique

    NASA Astrophysics Data System (ADS)

    Zhao, Guangdong; Chen, Bo; Chen, Longwei; Liu, Jianxin; Ren, Zhengyong

    2018-03-01

    The 3D Fourier forward modeling of 3D density sources is capable of providing 3D gravity anomalies coincided with the meshed density distribution within the whole source region. This paper firstly derives a set of analytical expressions through employing 3D Fourier transforms for calculating the gravity anomalies of a 3D density source approximated by right rectangular prisms. To reduce the errors due to aliasing and imposed periodicity as well as edge effects in the Fourier domain modeling, we develop the 3D Gauss-FFT technique to the 3D gravity anomalies forward modeling. The capability and adaptability of this scheme are tested by simple synthetic models. The results show that the accuracy of the Fourier forward methods using the Gauss-FFT with 4 Gaussian-nodes (or more) is comparable to that of the spatial modeling. In addition, the "ghost" source effects in the 3D Fourier forward gravity field due to imposed periodicity of the standard FFT algorithm are remarkably depressed by the application of the 3D Gauss-FFT algorithm. More importantly, the execution times of the 4 nodes Gauss-FFT modeling are reduced by two orders of magnitude compared with the spatial forward method. It demonstrates that the improved Fourier method is an efficient and accurate forward modeling tool for the gravity field.

  16. A Guided Tour of Mathematical Methods for the Physical Sciences

    NASA Astrophysics Data System (ADS)

    Snieder, Roel; van Wijk, Kasper

    2015-05-01

    1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

  17. Demystifying Electric Flux and Gauss's Law

    ERIC Educational Resources Information Center

    McManus, Jeff

    2017-01-01

    Many physics students have experienced the difficulty of internalizing concepts in electrostatics. After studying concrete, measurable details in mechanics, they are challenged by abstract ideas such as electric fields, flux, Gauss's law, and electric potential. There are a few well-known hands-on activities that help students get experience with…

  18. New class of generalized photon-added coherent states and some of their non-classical properties

    NASA Astrophysics Data System (ADS)

    Mojaveri, B.; Dehghani, A.; Mahmoodi, S.

    2014-08-01

    In this paper, we construct a new class of generalized photon added coherent states (GPACSs), |z,m{{\\rangle }_{r}} by excitations on a newly introduced family of generalized coherent states (GCSs) |z{{\\rangle }_{r}} (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwal's photon-added coherent states (PACSs), \\left| z,m \\right\\rangle .

  19. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

    NASA Astrophysics Data System (ADS)

    Tahir, Madeeha; Naeem, Muhammad Nawaz; Javaid, Maria; Younas, Muhammad; Imran, Muhammad; Sadiq, Naeem; Safdar, Rabia

    2018-04-01

    In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

  20. Dynamics of Proton Spin: Role of qqq Force

    NASA Astrophysics Data System (ADS)

    Mitra, A. N.

    The analytic structure of the qqq wave function, obtained recently in the high momentum regime of QCD, is employed for the formulation of baryonic transition amplitudes via quark loops. A new aspect of this study is the role of a direct (Y -shaped, Mercedes-Benz type) qqq force in generating the qqq wave function The dynamics is that of a Salpeter-like equation (3D support for the kernel) formulated covariantly on the light front, a la Markov-Yukawa Transversality Principle (MYTP) which warrants a 2-way interconnection between the 3D and 4D Bethe-Salpeter (BSE) forms for 2 as well as 3 fermion quarks. The dynamics of this 3-body force shows up through a characteristic singularity in the hypergeometric differential equation for the 3D wave function ϕ, corresponding to a negative eigenvalue of the spin operator iσ1·σ2 × σ3 which is an integral part of the qqq force. As a first application of this wave function to the problem of the proton spin anomaly, the two-gluon contribution to the anomaly yields an estimate of the right sign, although somewhat smaller in magnitude.

  1. Analytical time-domain Green’s functions for power-law media

    PubMed Central

    Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

    2008-01-01

    Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

  2. Algorithms for Nonlinear Least-Squares Problems

    DTIC Science & Technology

    1988-09-01

    O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

  3. Optically phase-locked electronic speckle pattern interferometer system performance for vibration measurement in random displacement fields

    NASA Astrophysics Data System (ADS)

    Moran, Steve E.; Lugannani, Robert; Craig, Peter N.; Law, Robert L.

    1989-02-01

    An analysis is made of the performance of an optically phase-locked electronic speckle pattern interferometer in the presence of random noise displacements. Expressions for the phase-locked speckle contrast for single-frame imagery and the composite rms exposure for two sequentially subtracted frames are obtained in terms of the phase-locked composite and single-frame fringe functions. The noise fringe functions are evaluated for stationary, coherence-separable noise displacements obeying Gauss-Markov temporal statistics. The theoretical findings presented here are qualitatively supported by experimental results.

  4. Pre-correction of distorted Bessel-Gauss beams without wavefront detection

    NASA Astrophysics Data System (ADS)

    Fu, Shiyao; Wang, Tonglu; Zhang, Zheyuan; Zhai, Yanwang; Gao, Chunqing

    2017-12-01

    By utilizing the property of the phase's rapid solution of the Gerchberg-Saxton algorithm, we experimentally demonstrate a scheme to correct distorted Bessel-Gauss beams resulting from inhomogeneous media as weak turbulent atmosphere with good performance. A probe Gaussian beam is employed and propagates coaxially with the Bessel-Gauss modes through the turbulence. No wavefront sensor but a matrix detector is used to capture the probe Gaussian beams, and then, the correction phase mask is computed through inputting such probe beam into the Gerchberg-Saxton algorithm. The experimental results indicate that both single and multiplexed BG beams can be corrected well, in terms of the improvement in mode purity and the mitigation of interchannel cross talk.

  5. The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane

    NASA Astrophysics Data System (ADS)

    Kuang, Xiao-Mei; Saavedra, Joel; Övgün, Ali

    2017-09-01

    We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing.

  6. High-power CO(2) laser with a Gauss-core resonator for high-speed cutting of thin metal sheets.

    PubMed

    Takenaka, Y; Nishimae, J; Tanaka, M; Motoki, Y

    1997-01-01

    A novel resonator, the Gauss-core resonator, based on a stable resonator configuration designed to yield a highly focusing beam operating in a large-volume TEM(00) mode, is presented. A 6.2 kW linearly polarized output beam with an M(2) factor of 1.7 is obtained experimentally for a high-power cw CO(2) laser. The capability of the Gauss-core resonator to process laser materials is also studied. We can cut 1-mm-thick mild (soft) steel with a maximum cutting speed of 58 m/min at 5.6 kW and 0.2-mm-thick steel 145 m/min at 2.8 kW.

  7. Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

    2013-09-01

    In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

  8. Galileo, Gauss, and the Green Monster

    ERIC Educational Resources Information Center

    Kalman, Dan; Teague, Daniel J.

    2013-01-01

    Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

  9. An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic

    ERIC Educational Resources Information Center

    Smith, Luke; Powell, Joan

    2011-01-01

    When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

  10. The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

    NASA Astrophysics Data System (ADS)

    Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

    2004-03-01

    Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

  11. From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo

    2014-12-01

    The entropy-maximization paradigm of statistical physics is well known to generate the omnipresent Gauss law. In this paper we establish an analogous socioeconomic model which maximizes social equality, rather than physical disorder, in the context of the distributions of income and wealth in human societies. We show that-on a logarithmic scale-the Laplace law is the socioeconomic equality-maximizing counterpart of the physical entropy-maximizing Gauss law, and that this law manifests an optimized balance between two opposing forces: (i) the rich and powerful, striving to amass ever more wealth, and thus to increase social inequality; and (ii) the masses, struggling to form more egalitarian societies, and thus to increase social equality. Our results lead from log-Gauss statistics to log-Laplace statistics, yield Paretian power-law tails of income and wealth distributions, and show how the emergence of a middle-class depends on the underlying levels of socioeconomic inequality and variability. Also, in the context of asset-prices with Laplace-distributed returns, our results imply that financial markets generate an optimized balance between risk and predictability.

  12. On the frequency spectra of the core magnetic field Gauss coefficients

    NASA Astrophysics Data System (ADS)

    Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias

    2018-03-01

    From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.

  13. On Nonconvex Decentralized Gradient Descent

    DTIC Science & Technology

    2016-08-01

    and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features, Math . Program., 116: 5-16, 2009. [2] H...splitting, and regularized Gauss-Seidel methods, Math . Pro- gram., Ser. A, 137: 91-129, 2013. [3] P. Bianchi and J. Jakubowicz, Convergence of a multi-agent...subgradient method under random communication topologies , IEEE J. Sel. Top. Signal Process., 5:754-771, 2011. [11] A. Nedic and A. Ozdaglar, Distributed

  14. Modeling radiative transfer with the doubling and adding approach in a climate GCM setting

    NASA Astrophysics Data System (ADS)

    Lacis, A. A.

    2017-12-01

    The nonlinear dependence of multiply scattered radiation on particle size, optical depth, and solar zenith angle, makes accurate treatment of multiple scattering in the climate GCM setting problematic, due primarily to computational cost issues. In regard to the accurate methods of calculating multiple scattering that are available, their computational cost is far too prohibitive for climate GCM applications. Utilization of two-stream-type radiative transfer approximations may be computationally fast enough, but at the cost of reduced accuracy. We describe here a parameterization of the doubling/adding method that is being used in the GISS climate GCM, which is an adaptation of the doubling/adding formalism configured to operate with a look-up table utilizing a single gauss quadrature point with an extra-angle formulation. It is designed to closely reproduce the accuracy of full-angle doubling and adding for the multiple scattering effects of clouds and aerosols in a realistic atmosphere as a function of particle size, optical depth, and solar zenith angle. With an additional inverse look-up table, this single-gauss-point doubling/adding approach can be adapted to model fractional cloud cover for any GCM grid-box in the independent pixel approximation as a function of the fractional cloud particle sizes, optical depths, and solar zenith angle dependence.

  15. Remote sensing of the magnetic moment of uranus: predictions for voyager.

    PubMed

    Hill, T W; Dessler, A J

    1985-03-22

    Power is supplied to a planet's magnetosphere from the kinetic energy of planetary spin and the energy flux of the impinging solar wind. A fraction of this power is available to drive numerous observable phenomena, such as polar auroras and planetary radio emissions. In this report our present understanding of these power transfer mechanisms is applied to Uranus to make specific predictions of the detectability of radio and auroral emissions by the planetary radio astronomy (PRA) and ultraviolet spectrometer (UVS) instruments aboard the Voyager spacecraft before its encounter with Uranus at the end of January 1986. The power available for these two phenomena is (among other factors) a function of the magnetic moment of Uranus. The date of earliest detectability also depends on whether the predominant power source for the magnetosphere is planetary spin or solar wind. The magnetic moment of Uranus is derived for each power source as a function of the date of first detection of radio emissions by the PRA instrument or auroral emissions by the UVS instrument. If we accept the interpretation of ultraviolet observations now available from the Earth-orbiting International Ultraviolet Explorer satellite, Uranus has a surface magnetic field of at least 0.6 gauss, and more probably several gauss, making it the largest or second-largest planetary magnetic field in the solar system.

  16. [Initial studies of the application of the linear signal transfer theory in evaluating diaphanoscopic examinations exemplified by rheumatism diagnosis].

    PubMed

    Beuthan, J; Cappius, H J; Hielscher, A; Hopf, M; Klose, A; Netz, U

    2001-11-01

    Rheumatoid arthritis affecting the small joints--in particular the fingers--has advantageous geometry for the transmission of near-infrared (NIR) light. Examination of the optical properties of tissues has revealed that as a result of changes to the capsule and synovial fluid there is a considerable increase in photon scattering already in the early stages of the disease--in particular around 685 nm. This suggests the appropriateness of analysing the photon density profile resulting from punctiform irradiation of the joint. In a first approximation, the point spread function of transmitted photon density is confirmed to be proportional to a Gauss distribution, as suggested by Arridge. In accordance with the linear signal transfer theory, therefore, it is possible to establish a virtual transfer system described by a first-order differential equation. (The tissue optical conditions mu a < mu's and mu a = constant (mu a = absorption coefficient) were assumed). The parameter mu's (= reduced scattering coefficient) was determined by linear approximation of the Gauss distribution to the calculated or measured point spread function. For selected patient data, the mu's was determined in healthy and diseased finger joints (e.g. 10.1 cm-1 and 26.8 cm-1, respectively), and the results were in good agreement with those obtained experimentally.

  17. Discrete shaped strain sensors for intelligent structures

    NASA Technical Reports Server (NTRS)

    Andersson, Mark S.; Crawley, Edward F.

    1992-01-01

    Design of discrete, highly distributed sensor systems for intelligent structures has been studied. Data obtained indicate that discrete strain-averaging sensors satisfy the functional requirements for distributed sensing of intelligent structures. Bartlett and Gauss-Hanning sensors, in particular, provide good wavenumber characteristics while meeting the functional requirements. They are characterized by good rolloff rates and positive Fourier transforms for all wavenumbers. For the numerical integration schemes, Simpson's rule is considered to be very simple to implement and consistently provides accurate results for five sensors or more. It is shown that a sensor system that satisfies the functional requirements can be applied to a structure that supports mode shapes with purely sinusoidal curvature.

  18. The Gauss and Ampere Laws: Different Laws but Similar Difficulties for Student Learning

    ERIC Educational Resources Information Center

    Guisasola, Jenaro; Almudi, Jose M.; Salinas, Julia; Zuza, Kristina; Ceberio, Mikel

    2008-01-01

    This study aims to analyse university students' reasoning regarding two laws of electromagnetism: Gauss's law and Ampere's law. It has been supposed that the problems seen in understanding and applying both laws do not spring from students' misconceptions. Students habitually use reasoning known in the literature as 'common sense' methodology that…

  19. Understanding Gauss's Law Using Spreadsheets

    ERIC Educational Resources Information Center

    Baird, William H.

    2013-01-01

    Some of the results from the electrostatics portion of introductory physics are particularly difficult for students to understand and/or believe. For students who have yet to take vector calculus, Gauss's law is far from obvious and may seem more difficult than Coulomb's. When these same students are told that the minimum potential…

  20. Explorations of the Gauss-Lucas Theorem

    ERIC Educational Resources Information Center

    Brilleslyper, Michael A.; Schaubroeck, Beth

    2017-01-01

    The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

  1. Theory and Programs for Dynamic Modeling of Tree Rings from Climate

    Treesearch

    Paul C. van Deusen; Jennifer Koretz

    1988-01-01

    Computer programs written in GAUSS(TM) for IBM compatible personal computers are described that perform dynamic tree ring modeling with climate data; the underlying theory is also described. The programs and a separate users manual are available from the authors, although users must have the GAUSS software package on their personal computer. An example application of...

  2. Block Gauss elimination followed by a classical iterative method for the solution of linear systems

    NASA Astrophysics Data System (ADS)

    Alanelli, Maria; Hadjidimos, Apostolos

    2004-02-01

    In the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the Gauss elimination process in the hope that this will increase the rates of convergence of the iterative method. This combination of methods has been proven successful especially when the matrix A of the system is an M-matrix. The purpose of this paper is to extend the idea of one to more Gauss elimination steps, consider other classes of matrices A, e.g., p-cyclic consistently ordered, and generalize and improve the asymptotic convergence rates of some of the methods known so far.

  3. Quintessence background for 5D Einstein-Gauss-Bonnet black holes

    NASA Astrophysics Data System (ADS)

    Ghosh, Sushant G.; Amir, Muhammed; Maharaj, Sunil D.

    2017-08-01

    As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r=r_C, with the stable (unstable) branch for r < (>) r_C.

  4. Hong-Ou-Mandel interference of entangled Hermite-Gauss modes

    NASA Astrophysics Data System (ADS)

    Zhang, Yingwen; Prabhakar, Shashi; Rosales-Guzmán, Carmelo; Roux, Filippus S.; Karimi, Ebrahim; Forbes, Andrew

    2016-09-01

    Hong-Ou-Mandel (HOM) interference is demonstrated experimentally for entangled photon pairs in the Hermite-Gauss (HG) basis. We use two Dove prisms in one of the paths of the photons to manipulate the entangled quantum state that enters the HOM interferometer. It is demonstrated that, when entangled photon pairs are in a symmetric Bell state in the Laguerre-Gauss (LG) basis, they will remain symmetric after decomposing them into the HG basis, thereby resulting in no coincidence events after the HOM interference. On the other hand, if the photon pairs are in an antisymmetric Bell state in the LG basis, then they will also be antisymmetric in the HG basis, thereby producing only coincidence events as a result of the HOM interference.

  5. Improved algorithm for calculating the Chandrasekhar function

    NASA Astrophysics Data System (ADS)

    Jablonski, A.

    2013-02-01

    Theoretical models of electron transport in condensed matter require an effective source of the Chandrasekhar H(x,omega) function. A code providing the H(x,omega) function has to be both accurate and very fast. The current revision of the code published earlier [A. Jablonski, Comput. Phys. Commun. 183 (2012) 1773] decreased the running time, averaged over different pairs of arguments x and omega, by a factor of more than 20. The decrease of the running time in the range of small values of the argument x, less than 0.05, is even more pronounced, reaching a factor of 30. The accuracy of the current code is not affected, and is typically better than 12 decimal places. New version program summaryProgram title: CHANDRAS_v2 Catalogue identifier: AEMC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 976 No. of bytes in distributed program, including test data, etc.: 11416 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any computer with a Fortran 90 compiler Operating system: Windows 7, Windows XP, Unix/Linux RAM: 0.7 MB Classification: 2.4, 7.2 Catalogue identifier of previous version: AEMC_v1_0 Journal reference of previous version: Comput. Phys. Commun. 183 (2012) 1773 Does the new version supersede the old program: Yes Nature of problem: An attempt has been made to develop a subroutine that calculates the Chandrasekhar function with high accuracy, of at least 10 decimal places. Simultaneously, this subroutine should be very fast. Both requirements stem from the theory of electron transport in condensed matter. Solution method: Two algorithms were developed, each based on a different integral representation of the Chandrasekhar function. The final algorithm is edited by mixing these two algorithms by selecting ranges of the argument omega in which the performance is the fastest. Reasons for the new version: Some of the theoretical models describing electron transport in condensed matter need a source of the Chandrasekhar H function values with an accuracy of at least 10 decimal places. Additionally, calculations of this function should be as fast as possible since frequent calls to a subroutine providing this function are made (e.g., numerical evaluation of a double integral with a complicated integrand containing the H function). Both conditions were satisfied in the algorithm previously published [1]. However, it has been found that a proper selection of the quadrature in an integral representation of the Chandrasekhar function may considerably decrease the running time. By suitable selection of the number of abscissas in Gauss-Legendre quadrature, the execution time was decreased by a factor of more than 20. Simultaneously, the accuracy of results has not been affected. Summary of revisions: (1) As in previous work [1], two integral representations of the Chandrasekhar function, H(x,omega), were considered: the expression published by Dudarev and Whelan [2] and the expression published by Davidović et al. [3]. The algorithms implementing these representations were designated A and B, respectively. All integrals in these implementations were previously calculated using Romberg quadrature. It has been found, however, that the use of Gauss-Legendre quadrature considerably improved the performance of both algorithms. Two conditions have to be satisfied. (i) The number of abscissas, N, has to be rather large, and (ii) the abscissas and corresponding weights should be determined with accuracy as high as possible. The abscissas and weights are available for N=16, 20, 24, 32, 40, 48, 64, 80, and 96 with accuracy of 20 decimal places [4], and all these values were introduced into a new procedure GAUSS replacing procedure ROMBERG. Due to the fact that the implemented tables are rather extensive, they were recalculated using the Rybicki algorithm (Ref. [5], pp. 183-184) and rechecked. No errors or misprints were found. (2) In the integral representation of the H function derived by Davidović et al. [3], the positive root ν0 of the so-called dispersion function needs to be calculated with accuracy of at least 10 decimal places (see. Ref [6], pp. 61-64 and Ref. [1], Eqs. (5) and (29)). For small values of the argument omega and values of omega close to unity, the nonlinear equation in one unknown, ν0, can be solved analytically. New simple analytical expressions were derived here that can be efficiently used in calculations of the root. (3) The above modifications of the code considerably decreased the time of calculation of both algorithms A and B. The results are summarized in Fig. 1. The time of calculations is in fact the CPU time in microseconds for a computer equipped with an Inter Xeon processor (3.46 GHz) using Lahey-Fujitsu Fortran v. 7.2. Time of calculations of the H(x,omega) function averaged over different pairs of arguments x and omega. (a) 400 pairs uniformly distributed in the ranges 0<=x<=0.05 and 0<=omega<=1; (b) 400 pairs uniformly distributed in the ranges 0.05<=x<=1 and 0<=omega<=1. The shortest execution time averaged over values of the argument x exceeding 0.05 has been observed for algorithm B and Gauss-Legendre quadrature with the number of abscissas equal to 64 (23.2 μs). As compared with Romberg quadrature, the execution time was shortened by a factor of 22.5. For small x values, below 0.05, both algorithms A and B are considerably faster if Gauss-Legendre quadrature is used. For N=64, the average time of execution of algorithm B is decreased with respect to Romberg quadrature by a factor close to 30. However, in that range of argument x, algorithm A exhibits much faster performance. Furthermore, the average execution time of algorithm A, equal to about 100 μs, is practically independent of the number of abscissas N. (4) For Romberg quadrature, to optimize the performance, the mixed algorithm C was proposed in which algorithm A is used for argument x smaller than or equal to x0=0.4, while algorithm B is used for x larger than 0.4 [1]. For Gauss-Legendre quadrature, the limit x0 was found to depend on the number of abscissas N. For each value of N considered, the time of calculations of the H function was determined for pairs of arguments uniformly distributed in the ranges 0<=x<=0.05 and 0<=omega<=1, and for pairs of arguments uniformly distributed in the ranges 0.05<=x<=1 and 0<=omega<=1. As shown in Fig. 2 for N=64, algorithm A is faster than algorithm B for x smaller than or equal to 0.0225. Comparison of the running times of algorithms A and B. Open circles: algorithm B is faster than the algorithm A; full circles: algorithm A is faster than algorithm B. Thus, the value of x0=0.0225 is proposed for the mixed algorithm C when Gauss-Legendere quadrature with N=64 is used. Similar computer experiments performed for other values of N are summarized below. L N0 1 16 0.25 2 20 0.15 3 24 0.10 4 32 0.050 5 40 0.030 6 48 0.045 7 64 0.0225-Recommended 8 80 0.0125 9 96 0.020 The flag L is one of the input parameters for the subroutine GAUSS. In the programs implementing algorithms A, B, and C (CHANDRA, CHANDRB, and CHANDRC), Gauss-Legendre quadrature with N=64 is currently set. As follows from Fig. 1, algorithm B (and consequently algorithm C) is the fastest in that case. It is still possible to change the number of abscissas; the flag L then has to be modified in lines 165, 169, 185, 189, and 304 of program CHANDRAS_v2, and the value of x0 in line 111 has to be adjusted according to the table above. (5) The above modifications of the code did not affect the accuracy of the calculated Chandrasekhar function, as compared to the original code [1]. For the pairs of arguments shown in Fig. 2, the accuracy of the H function, calculated from algorithms A and B, reached at least 12 decimal digits; however, in the majority of cases, the accuracy is equal to 13 decimal digits. Restrictions: Two input parameters for the Chandrasekhar function, x and omega, are restricted to the ranges 0<=x<=1 and 0<=omega<=1, which is sufficient in numerous applications. Running time: between 15 and 100 μs for one pair of arguments of the Chandrasekhar function.

  6. Using Patterns of Summed Scores in Paper-and-Pencil Tests and Computer-Adaptive Tests to Detect Misfitting Item Score Patterns

    ERIC Educational Resources Information Center

    Meijer, Rob R.

    2004-01-01

    Two new methods have been proposed to determine unexpected sum scores on sub-tests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted p, was compared with a method where the probability for each score combination was calculated using a…

  7. Higher order derivatives of R-Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Das, Sourav; Swaminathan, A.

    2016-06-01

    In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

  8. Theoretical and experimental study of a new algorithm for factoring numbers

    NASA Astrophysics Data System (ADS)

    Tamma, Vincenzo

    The security of codes, for example in credit card and government information, relies on the fact that the factorization of a large integer N is a rather costly process on a classical digital computer. Such a security is endangered by Shor's algorithm which employs entangled quantum systems to find, with a polynomial number of resources, the period of a function which is connected with the factors of N. We can surely expect a possible future realization of such a method for large numbers, but so far the period of Shor's function has been only computed for the number 15. Inspired by Shor's idea, our work aims to methods of factorization based on the periodicity measurement of a given continuous periodic "factoring function" which is physically implementable using an analogue computer. In particular, we have focused on both the theoretical and the experimental analysis of Gauss sums with continuous arguments leading to a new factorization algorithm. The procedure allows, for the first time, to factor several numbers by measuring the periodicity of Gauss sums performing first-order "factoring" interfer ence processes. We experimentally implemented this idea by exploiting polychromatic optical interference in the visible range with a multi-path interferometer, and achieved the factorization of seven digit numbers. The physical principle behind this "factoring" interference procedure can be potentially exploited also on entangled systems, as multi-photon entangled states, in order to achieve a polynomial scaling in the number of resources.

  9. Hantush Well Function revisited

    NASA Astrophysics Data System (ADS)

    Veling, E. J. M.; Maas, C.

    2010-11-01

    SummaryIn this paper, we comment on some recent numerical and analytical work to evaluate the Hantush Well Function. We correct an expression found in a Comment by Nadarajah [Nadarajah, S., 2007. A comment on numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 338, 152-153] to a paper by Prodanoff et al. [Prodanoff, J.A., Mansur, W.J., Mascarenhas, F.C.B., 2006. Numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 318, 173-183]. We subsequently derived another analytic representation based on a generalized hypergeometric function in two variables and from the hydrological literature we cite an analytic representation by Hunt [Hunt, B., 1977. Calculation of the leaky aquifer function. Journal of Hydrology 33, 179-183]. We have implemented both representations and compared the results. Using a convergence accelerator Hunt's representation of Hantush Well Function is efficient and accurate. While checking our implementations we found that Bear's table of the Hantush Well Function [Bear, J., 1979. Hydraulics of Groundwater. McGraw-Hill, New York, Tables 8-6] contains a number of typographical errors that are not present in the original table published by Hantush [Hantush, M.S., 1956. Analysis of data from pumping tests in leaky aquifers. Transactions, American Geophysical Union 37, 702-714]. Finally, we offer a very fast approximation with a maximum relative error of 0.0033 for the parameter range in the table given by Bear.

  10. Cyclotron emission from AM Herculis

    NASA Technical Reports Server (NTRS)

    Chanmugam, G.

    1981-01-01

    The cyclotron absorption coefficients in the ordinary and extraordinary modes are calculated for the shock heated region of AM Her. The equations of radiative transfer are solved and the intensity of the emitted UV radiation determined as a function of angle. The average spectrum is shown to have deviations from the previously predicted Rayleigh-Jeans spectrum and the magnetic field of AM Her is deduced to be roughly 5 x 10 to the 7th power gauss.

  11. Electron-hole pairs generation rate estimation irradiated by isotope Nickel-63 in silicone using GEANT4

    NASA Astrophysics Data System (ADS)

    Kovalev, I. V.; Sidorov, V. G.; Zelenkov, P. V.; Khoroshko, A. Y.; Lelekov, A. T.

    2015-10-01

    To optimize parameters of beta-electrical converter of isotope Nickel-63 radiation, model of the distribution of EHP generation rate in semiconductor must be derived. By using Monte-Carlo methods in GEANT4 system with ultra-low energy electron physics models this distribution in silicon calculated and approximated with Gauss function. Maximal efficient isotope layer thickness and maximal energy efficiency of EHP generation were estimated.

  12. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

    PubMed Central

    Abd-Elhameed, W. M.

    2014-01-01

    This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

  13. Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam Carlitz I polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Ahmed, H. M.

    2005-12-01

    Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives Dpqf(x), and for the moments xellDpqf(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

  14. Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes

    NASA Astrophysics Data System (ADS)

    Konoplya, R. A.; Zhidenko, A.

    2017-05-01

    Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

  15. On the properties of circular beams: normalization, Laguerre-Gauss expansion, and free-space divergence.

    PubMed

    Vallone, Giuseppe

    2015-04-15

    Circular beams were introduced as a very general solution to the paraxial wave equation carrying orbital angular momentum. Here, we study their properties by looking at their normalization and their expansion in terms of Laguerre-Gauss modes. We also study their far-field divergence and, for particular cases of the beam parameters, their possible experimental generation.

  16. Creating aperiodic photonic structures by synthesized Mathieu-Gauss beams

    NASA Astrophysics Data System (ADS)

    Vasiljević, Jadranka M.; Zannotti, Alessandro; Timotijević, Dejan V.; Denz, Cornelia; Savić, Dragana M. Jović

    2017-08-01

    We demonstrate a kind of aperiodic photonic structure realized using the interference of multiple Mathieu-Gauss beams. Depending on the beam configurations, their mutual distances, angles of rotation, or phase relations we are able to observe different classes of such aperiodic optically induced refractive index structures. Our experimental approach is based on the optical induction in a single parallel writing process.

  17. [Relationship between Copenhagen and Göttingen regarding earth magnetism].

    PubMed

    Reich, Karin

    2013-01-01

    Hans Christian Oersted is mostly known as the discoverer of electromagnetism and for being one of the physicists who were deeply influenced and fascinated by the romantic natural philosophy. In this article another side of Oersted is presented. What is underestimated until now is Oersted's contribution to the research of geomagnetism. Oersted stood in close contact with Carl Friedrich Gauss and Wilhelm Weber, whom he visited in 1834 in Göttingen. Oersted's aim was to learn the new developments in geomagnetism. Afterwards he was crucial in the building of a new magnetic observatory in Copenhagen as well as a second one with better equipment. Oersted formed a huge team for magnetic observations and the gathered data were sent to Gauss and Weber who published them. The correspondence between Oersted, Gauss and Weber was mostly dedicated to the transmission of these data, details about instruments and the best way of building a magnetic observatory. Unfortunately, Gauss and Weber had to stop their very successful collaboration in 1843, because Weber belonged to the Göttingen Seven and later on Oersted stopped his observations, because he had lost his partners in this research project.

  18. Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

    NASA Astrophysics Data System (ADS)

    Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben

    2018-04-01

    We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

  19. The generation of magnetic fields in astrophysical bodies. X - Magnetic buoyancy and the solar dynamo

    NASA Technical Reports Server (NTRS)

    Parker, E. N.

    1975-01-01

    The magnetic field appearing as bipolar magnetic regions at the surface of the sun represents the lines of force from a general azimuthal field of the order of 100 gauss somewhere beneath the surface. The amplification time, as a consequence of the nonuniform rotation, is of the order of 10 years. But magnetic buoyancy brings the azimuthal field up through much of the convective zone in a time rather less than 10 years, raising the question of where the azimuthal field can be retained long enough to be amplified. We show that magnetic fields can be retained for long periods of time in the stable radiative region beneath the convective zone, but unfortunately the solar dynamo cannot function there because turbulent diffusion is an essential part of its operation. The only possible conclusion appears to be that the dynamo operates principally in the very lowest levels of the convective zone at depths of 150,000 km or more, where the gas density is 0.1 g/cu cm, and the fields are limited to 50 gauss.

  20. Shear Recovery Accuracy in Weak-Lensing Analysis with the Elliptical Gauss-Laguerre Method

    NASA Astrophysics Data System (ADS)

    Nakajima, Reiko; Bernstein, Gary

    2007-04-01

    We implement the elliptical Gauss-Laguerre (EGL) galaxy-shape measurement method proposed by Bernstein & Jarvis and quantify the shear recovery accuracy in weak-lensing analysis. This method uses a deconvolution fitting scheme to remove the effects of the point-spread function (PSF). The test simulates >107 noisy galaxy images convolved with anisotropic PSFs and attempts to recover an input shear. The tests are designed to be immune to statistical (random) distributions of shapes, selection biases, and crowding, in order to test more rigorously the effects of detection significance (signal-to-noise ratio [S/N]), PSF, and galaxy resolution. The systematic error in shear recovery is divided into two classes, calibration (multiplicative) and additive, with the latter arising from PSF anisotropy. At S/N > 50, the deconvolution method measures the galaxy shape and input shear to ~1% multiplicative accuracy and suppresses >99% of the PSF anisotropy. These systematic errors increase to ~4% for the worst conditions, with poorly resolved galaxies at S/N simeq 20. The EGL weak-lensing analysis has the best demonstrated accuracy to date, sufficient for the next generation of weak-lensing surveys.

  1. Ricci-Gauss-Bonnet holographic dark energy

    NASA Astrophysics Data System (ADS)

    Saridakis, Emmanuel N.

    2018-03-01

    We present a model of holographic dark energy in which the infrared cutoff is determined by both the Ricci and the Gauss-Bonnet invariants. Such a construction has the significant advantage that the infrared cutoff, and consequently the holographic dark energy density, does not depend on the future or the past evolution of the universe, but only on its current features, and moreover it is determined by invariants, whose role is fundamental in gravitational theories. We extract analytical solutions for the behavior of the dark energy density and equation-of-state parameters as functions of the redshift. These reveal the usual thermal history of the universe, with the sequence of radiation, matter and dark energy epochs, resulting in the future to a complete dark energy domination. The corresponding dark energy equation-of-state parameter can lie in the quintessence or phantom regime, or experience the phantom-divide crossing during the cosmological evolution, and its asymptotic value can be quintessencelike, phantomlike, or be exactly equal to the cosmological-constant value. Finally, we extract the constraints on the model parameters that arise from big bang nucleosynthesis.

  2. Studies on probe measurements in presence of magnetic field in dust containing hydrogen plasma

    NASA Astrophysics Data System (ADS)

    Kalita, Deiji; Kakati, Bharat; Kausik, Siddhartha Sankar; Saikia, Bipul Kumar; Bandyopadhyay, Mainak

    2018-04-01

    The accuracy of plasma parameters measured by Langmuir probe in presence of magnetic field is studied in our present work. It is observed that the ratio of electron to ion saturation current shows almost identical behavior with that of unmagnetized hydrogen plasma when r L > 10 r p (here r L : Larmor radius and r p : probe radius). At magnetic field strength, B = 594 gauss, the electron temperature ( T e ) shows an overestimated value up to 35-40%, whereas at B ≤ 37 gauss, T e shows around ≤10% overestimated value w.r.t. unmagnetized case. A bi-Maxwellian electron energy probability function is observed for entire magnetic field range for both pristine and dust containing hydrogen plasma. The bulk (cold) electron collection by the Langmuir probe is strongly suppressed whereas the higher energetic electron collection remains unaffected in presence of magnetic field. In presence of dust grains, it is found that the low energy electron population decreases even more than the magnetized plasma and the high-energy tail slightly increases compared to the pristine plasma.

  3. The preconditioned Gauss-Seidel method faster than the SOR method

    NASA Astrophysics Data System (ADS)

    Niki, Hiroshi; Kohno, Toshiyuki; Morimoto, Munenori

    2008-09-01

    In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10

  4. Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

    PubMed

    Hudson, H M; Ma, J; Green, P

    1994-01-01

    Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

  5. Ince's limits for confluent and double-confluent Heun equations

    NASA Astrophysics Data System (ADS)

    Bonorino Figueiredo, B. D.

    2005-11-01

    We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for ∣z∣>∣z0∣, where z0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schrödinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.

  6. Kicking the rugby ball: perturbations of 6D gauged chiral supergravity

    NASA Astrophysics Data System (ADS)

    Burgess, C. P.; de Rham, C.; Hoover, D.; Mason, D.; Tolley, A. J.

    2007-02-01

    We analyse the axially symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find that all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the non-conical ones for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped 'rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.

  7. Multichannel conformal blocks for scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Belitsky, A. V.

    2018-05-01

    By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type.

  8. A bispectral q-hypergeometric basis for a class of quantum integrable models

    NASA Astrophysics Data System (ADS)

    Baseilhac, Pascal; Martin, Xavier

    2018-01-01

    For the class of quantum integrable models generated from the q-Onsager algebra, a basis of bispectral multivariable q-orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q-Onsager algebra, whose fundamental generators are realized in terms of the multivariable q-difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q-Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q-hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).

  9. 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

    NASA Astrophysics Data System (ADS)

    Jahandari, H.; Farquharson, C. G.

    2017-11-01

    Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

  10. Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Grandi, Nicolás; Landea, Ignacio Salazar

    2018-02-01

    We explore charged black hole solutions in Einstein-Gauss-Bonnet gravity in five dimensions, with a charged scalar hair. We interpret such hairy black holes as the final state of the superradiant instability previously reported for this system. We explore the relation of the hairy black hole solutions with the nonbackreacting quasibound states and scalar clouds, as well as with the boson star solutions.

  11. Security Engineering Project

    DTIC Science & Technology

    2015-01-31

    from a wireless joystick console broadcasting at 2.4 GHz. Figure 6. GTRI Airborne Unmanned Sensor System As shown in Figure 7 the autopilot has a...generating wind turbines , and video reconnaissance systems on unmanned aerial vehicles (UAVs). The most basic decision problem in designing a...chosen test UAV case was the GTRI Aerial Unmanned Sensor System (GAUSS) aircraft. The GAUSS platform is a small research UAV with a widely used

  12. Clinical Profile of Statin Intolerance in the Phase 3 GAUSS-2 Study.

    PubMed

    Cho, Leslie; Rocco, Michael; Colquhoun, David; Sullivan, David; Rosenson, Robert S; Dent, Ricardo; Xue, Allen; Scott, Rob; Wasserman, Scott M; Stroes, Erik

    2016-06-01

    Recent evidence suggests that statin intolerance may be more common than reported in randomized trials. However, the statin-intolerant population is not well characterized. The goal of this report is to characterize the population enrolled in the phase 3 Goal Achievement after Utilizing an anti-PCSK9 antibody in Statin Intolerant Subjects Study (GAUSS-2; NCT 01763905). GAUSS-2 compared evolocumab, a fully human monoclonal antibody to proprotein convertase subtilisin/kexin type 9 (PCSK9) to ezetimibe in hypercholesterolemic patients who discontinued statin therapy due to statin-associated muscle symptoms (SAMS). GAUSS-2 was a 12-week, double-blind, placebo-controlled, randomized study that enrolled patients with elevated LDL-C who were either not on a statin or able to tolerate only a low-dose due to SAMS. Patients had received ≥2 statins and were unable to tolerate any statin dose or increase in dose above a specified weekly dose due to SAMS. Three hundred seven patients (mean [SD] age, 62 [10] years; 54 % males) were randomized 2:1 (evolocumab:ezetimibe). Mean (SD) LDL-C was 4.99 (1.51) mmol/L. Patients had used ≥2 (100 %), ≥3 (55 %), or ≥4 (21 %) statins. Coronary artery disease was present in 29 % of patients. Statin-intolerant symptoms were myalgia in 80 % of patients, weakness in 39 %, and more serious complications in 20 %. In 98 % of patients, SAMS interfered with normal daily activity; in 52 %, symptoms precluded moderate exertion. Evaluation of the GAUSS-2 trial population of statin-intolerant patients demonstrates that most patients were high risk with severely elevated LDL-C and many had statin-associated muscle symptoms that interfered with their quality of life.

  13. Spontaneous generation of vortex and coherent vector beams from a thin-slice c-cut Nd:GdVO4 laser with wide-aperture laser-diode end pumping: application to highly sensitive rotational and translational Doppler velocimetry

    NASA Astrophysics Data System (ADS)

    Otsuka, Kenju; Chu, Shu-Chun

    2017-07-01

    Selective excitation of Laguerre-Gauss modes (optical vortices: helical LG0,2 and LG0,1), reflecting their weak transverse cross-saturation of population inversions against a preceding higher-order Ince-Gauss (IG0,2) or Hermite-Gauss (HG2,1) mode, was observed in a thin-slice c-cut Nd:GdVO4 laser with wide-aperture laser-diode end pumping. Single-frequency coherent vector beams were generated through the transverse mode locking of a pair of orthogonally polarized IG2,0 and LG0,2 or HG2,1 and LG0,1 modes. Highly sensitive self-mixing rotational and translational Doppler velocimetry is demonstrated by using vortex and coherent vector beams.

  14. Simulation of fluid-structure interaction in micropumps by coupling of two commercial finite element programs

    NASA Astrophysics Data System (ADS)

    Klein, Andreas; Gerlach, Gerald

    1998-09-01

    This paper deals with the simulation of the fluid-structure interaction phenomena in micropumps. The proposed solution approach is based on external coupling of two different solvers, which are considered here as `black boxes'. Therefore, no specific intervention is necessary into the program code, and solvers can be exchanged arbitrarily. For the realization of the external iteration loop, two algorithms are considered: the relaxation-based Gauss-Seidel method and the computationally more extensive Newton method. It is demonstrated in terms of a simplified test case, that for rather weak coupling, the Gauss-Seidel method is sufficient. However, by simply changing the considered fluid from air to water, the two physical domains become strongly coupled, and the Gauss-Seidel method fails to converge in this case. The Newton iteration scheme must be used instead.

  15. Brane universes with Gauss-Bonnet-induced-gravity

    NASA Astrophysics Data System (ADS)

    Brown, Richard A.

    2007-04-01

    The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a “dark energy” field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density “Big-Bang” and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.

  16. Orbital angular momentum mode of Gaussian beam induced by atmospheric turbulence

    NASA Astrophysics Data System (ADS)

    Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Dong, Kangjun

    2018-02-01

    Superposition theory of the spiral harmonics is employed to numerical study the transmission property of the orbital angular momentum (OAM) mode of Gaussian beam induced by atmospheric turbulence. Results show that Gauss beam does not carry OAM at the source, but various OAM modes appear after affected by atmospheric turbulence. With the increase of atmospheric turbulence strength, the smaller order OAM modes appear firstly, followed by larger order OAM modes. The beam spreading of Gauss beams in the atmosphere enhance with the increasing topological charge of the OAM modes caused by atmospheric turbulence. The mode probability density of the OAM generated by atmospheric turbulence decreases, and peak position gradually deviate from the Gauss beam spot center with the increase of the topological charge. Our results may be useful for improving the performance of long distance laser digital spiral imaging system.

  17. Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

    NASA Astrophysics Data System (ADS)

    Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

    2010-03-01

    We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

  18. Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code

    NASA Astrophysics Data System (ADS)

    Diep, Do Ngoc; Giang, Do Hoang; Phu, Phan Huy

    2017-12-01

    The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMB (s a) = s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set √ {2^{|B|}}.

  19. Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code

    NASA Astrophysics Data System (ADS)

    Diep, Do Ngoc; Giang, Do Hoang; Phu, Phan Huy

    2018-03-01

    The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMB (s a)=s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set √ {2^{|B|}}.

  20. Rotation of large asymmetrical absorbing objects by Laguerre-Gauss beams.

    PubMed

    Herne, Catherine M; Capuzzi, Kristina M; Sobel, Emily; Kropas, Ryan T

    2015-09-01

    In this Letter, we show the manipulation and rotation of opaque graphite through adhesion with optically trapped polystyrene spheres. The absorbing graphite is rotated by the orbital angular momentum transfer from a Laguerre-Gauss laser mode and is trapped due to the presence of refracting spheres. This technique is effective for trapping and rotating absorbing objects of all sizes, including those larger than the laser mode.

  1. Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

    NASA Technical Reports Server (NTRS)

    Llorente, Ignacio M.; Melson, N. Duane

    1998-01-01

    We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

  2. On the Maximum-Weight Clique Problem.

    DTIC Science & Technology

    1985-06-01

    hypergeometric distribution", Discrete Math . 25, 285-287 .* CHVATAL, V. (1983), Linear Programming, W.H. Freeman, New York/San Francisco. COOK, S.A. (1971...Annals Discrete Math . 21, 325-356 GROTSCHEL, M., L. LOVASZ, and A. SCHRIJVER ((1984b), "Relaxations of Vertex Packing", Preprint No. 35...de Grenoble. See also N. Sbihi, "Algorithme de recherche d’un stable de cardinalite maximum dans un graphe sans etoile", Discrete Math . 19 (1980), 53

  3. An implementation problem for boson fields and quantum Girsanov transform

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp

    2016-08-15

    We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

  4. F-111C Flight Data Reduction and Analysis Procedures

    DTIC Science & Technology

    1990-12-01

    BPHI NO 24 BTHE YES 25 BPSI NO 26 BH YES 27 LVEL NO 28 LBET NO 29 LALP YES 30 LPHI NO 31 LTHE NO 32 LPSI NO 33 LH NO 34 TABLE 2 INPUTS I Ax YES 2 Av NO...03 * 51 IJ Appendix G - A priori Data from Six Degree of Free- dom Flight Dynamic Model The six degree of freedom flight dynamic mathematical model of...Estimated Mathematical mode response - > of aircraft !Gauss- Maximum " Newton --- likelihood 4,computational cost Salgorithm function Maximum

  5. Analysis of the Binary Euclidean Algorithm

    DTIC Science & Technology

    1976-06-01

    Probleme de Gauss," Atti del Congresso Internationale dei Matematici 6 (Bologna, 1928), 83-89. Levy [29] Levy, P., "Sur les Lois de Probabilite...r- Report) 11. SUPPL ENEN T A IllY NOTES lt . KEY WOI’IOS ( Continue on revere• ai de II nec:eaeary and Identify by bloc I< number) I 20...easily de - n n duced by differentiation. 3. The Distribution Functions F ’’ LI The following theorem gives the form of F (x) for finite n n

  6. Monterey Bay Geoid

    DTIC Science & Technology

    1994-03-01

    thought to be a flat disk. The first scientific hypothesis that the earth was spherical is credited to Thales of Milet in 600 B.C. or Pythagoras in 550...acceleration can be integrated over the surface, by Gauss’s theorem and gives: 35 v1 Wv2 <v3 Figure 12. Equipotential Surfaces and Gravity: V,, V2, V3 are...continuous derivatives where they satisfy Laplace’s equation. Stokes’ theorem states that a harmonic function outside a surface is uniquely determined by

  7. Decoding algorithm for vortex communications receiver

    NASA Astrophysics Data System (ADS)

    Kupferman, Judy; Arnon, Shlomi

    2018-01-01

    Vortex light beams can provide a tremendous alphabet for encoding information. We derive a symbol decoding algorithm for a direct detection matrix detector vortex beam receiver using Laguerre Gauss (LG) modes, and develop a mathematical model of symbol error rate (SER) for this receiver. We compare SER as a function of signal to noise ratio (SNR) for our algorithm and for the Pearson correlation algorithm. To our knowledge, this is the first comprehensive treatment of a decoding algorithm of a matrix detector for an LG receiver.

  8. An Application of the H-Function to Curve-Fitting and Density Estimation.

    DTIC Science & Technology

    1983-12-01

    equations into a model that is linear in its coefficients. Nonlinear least squares estimation is a relatively new area developed to accomodate models which...to converge on a solution (10:9-10). For the simple linear model and when general assump- tions are made, the Gauss-Markov theorem states that the...distribution. For example, if the analyst wants to model the time between arrivals to a queue for a computer simulation, he infers the true probability

  9. Optimal reconstruction angles

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cook, G.O. Jr.; Knight, L.

    1979-07-01

    The question of optimal projection angles has recently become of interest in the field of reconstruction from projections. Here, studies are concentrated on the n x n pixel space, where literative algorithms such as ART and direct matrix techniques due to Katz are considered. The best angles are determined in a Gauss--Markov statistical sense as well as with respect to a function-theoretical error bound. The possibility of making photon intensity a function of angle is also examined. Finally, the best angles to use in an ART-like algorithm are studied. A certain set of unequally spaced angles was found to bemore » preferred in several contexts. 15 figures, 6 tables.« less

  10. Smectic viral capsids and the aneurysm instability

    NASA Astrophysics Data System (ADS)

    Dharmavaram, S.; Rudnick, J.; Lawrence, C. M.; Bruinsma, R. F.

    2018-05-01

    The capsids of certain Archaea-infecting viruses undergo large shape changes, while maintaining their integrity against rupture by osmotic pressure. We propose that these capsids are in a smectic liquid crystalline state, with the capsid proteins assembling along spirals. We show that smectic capsids are intrinsically stabilized against the formation of localized bulges with non-zero Gauss curvature while still allowing for large-scale cooperative shape transformation that involves global changes in the Gauss curvature.

  11. Increasing reliability of Gauss-Kronrod quadrature by Eratosthenes' sieve method

    NASA Astrophysics Data System (ADS)

    Adam, Gh.; Adam, S.

    2001-04-01

    The reliability of the local error estimates returned by the Gauss-Kronrod quadrature rules can be raised up to the theoretical 100% rate of success, under error estimate sharpening, provided a number of natural validating conditions are required. The self-validating scheme of the local error estimates, which is easy to implement and adds little supplementary computing effort, strengthens considerably the correctness of the decisions within the automatic adaptive quadrature.

  12. Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

    DTIC Science & Technology

    2014-10-30

    Houzeaux et al., 2009). The GM- RES solver is also employed to solve for the enthalpy and species mass fractions. The Gauss - Seidel iterative method is...the system is therefore split to solve the mo- mentum and continuity equations independently. This is achieved by applying an iterative strategy...the momentum equation twice and the continuity equation once. The momentum equation is solved using the GMRES or BICGSTAB method (diagonal and Gauss

  13. Quantifying the Energy Efficiency of Object Recognition and Optical Flow

    DTIC Science & Technology

    2014-03-28

    other linear solvers, such as conjugate- gradient (CG), preconditioned conjugate-gradient (PCG), and red-black Gauss Seidel (RB). We have also... Seidel , and conjugate gradient solvers. We are interested in the energy it takes to get a given solution quality. In Figure 6, we plot the quality of...in terms of Joules. Conversely, our implementation of red-black Gauss Seidel proves to be very inefficient when we consider Joules instead of just

  14. Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?

    NASA Astrophysics Data System (ADS)

    Benincasa, Dionigi M. T.

    2011-07-01

    We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.

  15. Verification of Faulty Message Passing Systems with Continuous State Space in PVS

    NASA Technical Reports Server (NTRS)

    Pilotto, Concetta; White, Jerome

    2010-01-01

    We present a library of Prototype Verification System (PVS) meta-theories that verifies a class of distributed systems in which agent commu nication is through message-passing. The theoretic work, outlined in, consists of iterative schemes for solving systems of linear equations , such as message-passing extensions of the Gauss and Gauss-Seidel me thods. We briefly review that work and discuss the challenges in formally verifying it.

  16. Fractional Fourier transform of Lorentz-Gauss vortex beams

    NASA Astrophysics Data System (ADS)

    Zhou, GuoQuan; Wang, XiaoGang; Chu, XiuXiang

    2013-08-01

    An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

  17. Zeeman Tuning Rate for Q Branch Transitions in the v3 Band of NO2

    NASA Technical Reports Server (NTRS)

    Mahon, C. R.; Chackerian, C., Jr.; Gore, Warren J. Y. (Technical Monitor)

    1997-01-01

    Zeeman tuning rates have bee a measured for Q branch transitions in the v3 band of NO2(approx.1610/cm) for magnetic fields of up to 564 Gauss. The average measured tuning rate is 0.1815(53) x 10(exp -3)/cm/Gauss with no dependence on Ka within the approx. equal to 3% standard deviation. Despite significant ,pin-rotation interaction between several of the observed levels the result agrees with the simple linear model for Honda case (be molecules (tuning rate = 2muogs = 0.18696 x 10(exp -3)/cm/Gauss) which neglects the spin-rotation interaction between different J states. The Zeeman effect is analyzed in a full treatment of the Hamiltonian, including spin-rotation interaction, in order to account for the agreement with 2muogs and to explore the onset of spin-rotation effects in the spectra as the magnetic field is increased.

  18. Summary of initial results from the GSFC fluxgate magnetometer on Pioneer 11

    NASA Technical Reports Server (NTRS)

    Acuna, M. H.; Ness, N. F.

    1975-01-01

    The main magnetic field of Jupiter was measured by the Fluxgate Magnetometer on Pioneer 11 and analysis reveals it to be relatively more complex than expected. In a centered spherical harmonic representation with a maximum order of n = 3 (designated GSFC model 04), the dipole term (with opposite polarity to the Earth's) has a moment of 4.28 Gauss x (Jupiter radius cubed), tilted by 9.6 deg towards a system 111 longitude of 232. The quadrupole and octupole moments are significant, 24% and 21% of the dipole moment respectively, and this leads to deviations of the planetary magnetic field from a simple offset tilted dipole for distances smaller than three Jupiter radii. The GSFC model shows a north polar field strength of 14 Gauss and a south polar field strength of 10.4 Gauss. Enhanced absorption effects in the radiation belts may be predicted as a result of field distortion.

  19. Derivation of the Lorentz force law, the magnetic field concept and the Faraday Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

    NASA Astrophysics Data System (ADS)

    Field, J. H.

    2006-06-01

    It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space time and energy momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

  20. A note on the preconditioner Pm=(I+Sm)

    NASA Astrophysics Data System (ADS)

    Kohno, Toshiyuki; Niki, Hiroshi

    2009-03-01

    Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have reported that the convergence rate of the iterative method with a preconditioner Pm=(I+Sm) was superior to one of the modified Gauss-Seidel method under the condition. These authors derived a theorem comparing the Gauss-Seidel method with the proposed method. However, through application of a counter example, Wen Li [Wen Li, A note on the preconditioned GaussSeidel (GS) method for linear systems, Journal of Computational and Applied Mathematics 182 (2005) 81-91] pointed out that there exists a special matrix that does not satisfy this comparison theorem. In this note, we analyze the reason why such a to counter example may be produced, and propose a preconditioner to overcome this problem.

  1. Two new modified Gauss-Seidel methods for linear system with M-matrices

    NASA Astrophysics Data System (ADS)

    Zheng, Bing; Miao, Shu-Xin

    2009-12-01

    In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

  2. Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

    NASA Astrophysics Data System (ADS)

    Yang, Xiang; Mittal, Rajat

    2017-03-01

    In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

  3. Phase space of modified Gauss-Bonnet gravity.

    PubMed

    Carloni, Sante; Mimoso, José P

    2017-01-01

    We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f ( R ) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.

  4. Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

    PubMed Central

    Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

    2012-01-01

    The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

  5. A homogeneous superconducting magnet design using a hybrid optimization algorithm

    NASA Astrophysics Data System (ADS)

    Ni, Zhipeng; Wang, Qiuliang; Liu, Feng; Yan, Luguang

    2013-12-01

    This paper employs a hybrid optimization algorithm with a combination of linear programming (LP) and nonlinear programming (NLP) to design the highly homogeneous superconducting magnets for magnetic resonance imaging (MRI). The whole work is divided into two stages. The first LP stage provides a global optimal current map with several non-zero current clusters, and the mathematical model for the LP was updated by taking into account the maximum axial and radial magnetic field strength limitations. In the second NLP stage, the non-zero current clusters were discretized into practical solenoids. The superconducting conductor consumption was set as the objective function both in the LP and NLP stages to minimize the construction cost. In addition, the peak-peak homogeneity over the volume of imaging (VOI), the scope of 5 Gauss fringe field, and maximum magnetic field strength within superconducting coils were set as constraints. The detailed design process for a dedicated 3.0 T animal MRI scanner was presented. The homogeneous magnet produces a magnetic field quality of 6.0 ppm peak-peak homogeneity over a 16 cm by 18 cm elliptical VOI, and the 5 Gauss fringe field was limited within a 1.5 m by 2.0 m elliptical region.

  6. Computational Fluid Dynamics for Atmospheric Entry

    DTIC Science & Technology

    2009-09-01

    equations. This method is a parallelizable variant of the Gauss - Seidel line-relaxation method of MacCormack (Ref. 33, 35), and is at the core of the...G.V. Candler, “The Solution of the Navier-Stokes Equations Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, 1989, pp. 135-150. 35... solution differs by 5% from the results obtained using the direct simulation Monte Carlo method . 3 Some authors advocate the use of higher-order continuum

  7. Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity.

    PubMed

    Chatterjee, Ayan; Sarkar, Sudipta

    2012-03-02

    We establish the physical process version of the first law by studying small perturbations of a stationary black hole with a regular bifurcation surface in Einstein-Gauss-Bonnet gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies the null energy condition.

  8. On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Wilson, Mitsuru

    2017-01-01

    We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

  9. Development of a Double-Gauss Lens Based Setup for Optoacoustic Applications

    PubMed Central

    Choi, Hojong; Ryu, Jae-Myung; Yeom, Jung-Yeol

    2017-01-01

    In optoacoustic (photoacoustic) systems, different echo signal intensities such as amplitudes, center frequencies, and bandwidths need to be compensated by utilizing variable gain or time-gain compensation amplifiers. However, such electronic components can increase system complexities and signal noise levels. In this paper, we introduce a double-Gauss lens to generate a large field of view with uniform light intensity due to the low chromatic aberrations of the lens, thus obtaining uniform echo signal intensities across the field of view of the optoacoustic system. In order to validate the uniformity of the echo signal intensities in the system, an in-house transducer was placed at various positions above a tissue sample and echo signals were measured and compared with each other. The custom designed double-Gauss lens demonstrated negligible light intensity variation (±1.5%) across the illumination field of view (~2 cm diameter). When the transducer was used to measure echo signal from an eye of a bigeye tuna within a range of ±1 cm, the peak-to-peak amplitude, center frequency, and their −6 dB bandwidth variations were less than 2 mV, 1 MHz, and 6%, respectively. The custom designed double-Gauss lens can provide uniform light beam across a wide area while generating insignificant echo signal variations, and thus can lower the burden of the receiving electronics or signal processing in the optoacoustic system. PMID:28273794

  10. A Bayesian mixture model for chromatin interaction data.

    PubMed

    Niu, Liang; Lin, Shili

    2015-02-01

    Chromatin interactions mediated by a particular protein are of interest for studying gene regulation, especially the regulation of genes that are associated with, or known to be causative of, a disease. A recent molecular technique, Chromatin interaction analysis by paired-end tag sequencing (ChIA-PET), that uses chromatin immunoprecipitation (ChIP) and high throughput paired-end sequencing, is able to detect such chromatin interactions genomewide. However, ChIA-PET may generate noise (i.e., pairings of DNA fragments by random chance) in addition to true signal (i.e., pairings of DNA fragments by interactions). In this paper, we propose MC_DIST based on a mixture modeling framework to identify true chromatin interactions from ChIA-PET count data (counts of DNA fragment pairs). The model is cast into a Bayesian framework to take into account the dependency among the data and the available information on protein binding sites and gene promoters to reduce false positives. A simulation study showed that MC_DIST outperforms the previously proposed hypergeometric model in terms of both power and type I error rate. A real data study showed that MC_DIST may identify potential chromatin interactions between protein binding sites and gene promoters that may be missed by the hypergeometric model. An R package implementing the MC_DIST model is available at http://www.stat.osu.edu/~statgen/SOFTWARE/MDM.

  11. Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow.

    PubMed

    Sachdeva, Himani; Barton, Nicholas H

    2017-06-01

    Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few-locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two-deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration-selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual-based simulations. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

  12. Modified parton branching model for multi-particle production in hadronic collisions: Application to SUSY particle branching

    NASA Astrophysics Data System (ADS)

    Yuanyuan, Zhang

    The stochastic branching model of multi-particle productions in high energy collision has theoretical basis in perturbative QCD, and also successfully describes the experimental data for a wide energy range. However, over the years, little attention has been put on the branching model for supersymmetric (SUSY) particles. In this thesis, a stochastic branching model has been built to describe the pure supersymmetric particle jets evolution. This model is a modified two-phase stochastic branching process, or more precisely a two phase Simple Birth Process plus Poisson Process. The general case that the jets contain both ordinary particle jets and supersymmetric particle jets has also been investigated. We get the multiplicity distribution of the general case, which contains a Hypergeometric function in its expression. We apply this new multiplicity distribution to the current experimental data of pp collision at center of mass energy √s = 0.9, 2.36, 7 TeV. The fitting shows the supersymmetric particles haven't participate branching at current collision energy.

  13. Supersymmetric Casimir energy and SL(3,Z) transformations

    NASA Astrophysics Data System (ADS)

    Brünner, Frederic; Regalado, Diego; Spiridonov, Vyacheslav P.

    2017-07-01

    We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an SL(3,Z) transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for N=1 SQCD and N=4 supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian N=2 SCFT with E6 flavour symmetry. Furthermore, we predict an expression for Casimir energy of the N=1 SP(2N) theory with SU(8) × U(1) flavour symmetry that is part of a multiple duality network, and for the doubled N=1 theory with enhanced E7 flavour symmetry.

  14. DOSE: an R/Bioconductor package for disease ontology semantic and enrichment analysis.

    PubMed

    Yu, Guangchuang; Wang, Li-Gen; Yan, Guang-Rong; He, Qing-Yu

    2015-02-15

    Disease ontology (DO) annotates human genes in the context of disease. DO is important annotation in translating molecular findings from high-throughput data to clinical relevance. DOSE is an R package providing semantic similarity computations among DO terms and genes which allows biologists to explore the similarities of diseases and of gene functions in disease perspective. Enrichment analyses including hypergeometric model and gene set enrichment analysis are also implemented to support discovering disease associations of high-throughput biological data. This allows biologists to verify disease relevance in a biological experiment and identify unexpected disease associations. Comparison among gene clusters is also supported. DOSE is released under Artistic-2.0 License. The source code and documents are freely available through Bioconductor (http://www.bioconductor.org/packages/release/bioc/html/DOSE.html). Supplementary data are available at Bioinformatics online. gcyu@connect.hku.hk or tqyhe@jnu.edu.cn. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

  15. Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams.

    PubMed

    Peet, Viktor

    2011-08-01

    For a light beam focused through a biaxial crystal along one of its optical axes, the effect of internal conical refraction in the crystal leads to the formation in the focal image plane of two bright rings separated by a dark ring. It is shown that, with circularly polarized Laguerre-Gauss LG(0)(ℓ) beams entering the crystal, this classical double-ring pattern is transformed into a multiring one consisting of ℓ+2 bright rings. © 2011 Optical Society of America

  16. A conservative staggered-grid Chebyshev multidomain method for compressible flows

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.; Kolias, John H.

    1995-01-01

    We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

  17. Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling.

    PubMed

    Silva, Hector O; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P; Berti, Emanuele

    2018-03-30

    We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.

  18. Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

    DTIC Science & Technology

    2014-01-14

    right-hand side is the only quadratic operation). The number of sub- iterations , kmax, used in this update needs to be chosen for optimal convergence and...Upper Symmetric Gauss - Seidel Method for the Euler and Navier-Stokes Equations,”, AIAA Journal, Vol. 26, No. 9, pp. 1025-1026, Sept. 1988. 11Edwards, J.R...Candler, “The Solution of the Navier-Stokes Equations Using Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, pp. 135-150, 1989

  19. The Battlefield Environment Division Modeling Framework (BMF). Part 1: Optimizing the Atmospheric Boundary Layer Environment Model for Cluster Computing

    DTIC Science & Technology

    2014-02-01

    idle waiting for the wavefront to reach it. To overcome this, Reeve et al. (2001) 3 developed a scheme in analogy to the red-black Gauss - Seidel iterative ...understandable procedure calls. Parallelization of the SIMPLE iterative scheme with SIP used a red-black scheme similar to the red-black Gauss - Seidel ...scheme, the SIMPLE method, for pressure-velocity coupling. The result is a slowing convergence of the outer iterations . The red-black scheme excites a 2

  20. Reduction of quantum systems and the local Gauss law

    NASA Astrophysics Data System (ADS)

    Stienstra, Ruben; van Suijlekom, Walter D.

    2018-05-01

    We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).

  1. Magnetism in the AM Herculis variable CW 1103+254

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schmidt, G.D.; Stockman, H.W.; Grandi, S.A.

    Time-resolved spectropolarimetry and spectrophotometry of the recently discovered magnetic binary CW 1103+254 reveal Zeeman-split Balmer polarization and absorption features corresponding to a mean photospheric field on the white dwarf primary of strength B = (19 +- 2) x 10/sup 6/ gauss. The orbital inclination i = 69/sup 0/ and latitude of the accreting magnetic pole ..delta.. = -56/sup 0/. With this perspective, we estimate the polar field strength B/sub p/ = (30 +- 5) x 10/sup 6/ gauss.

  2. NEAT: an efficient network enrichment analysis test.

    PubMed

    Signorelli, Mirko; Vinciotti, Veronica; Wit, Ernst C

    2016-09-05

    Network enrichment analysis is a powerful method, which allows to integrate gene enrichment analysis with the information on relationships between genes that is provided by gene networks. Existing tests for network enrichment analysis deal only with undirected networks, they can be computationally slow and are based on normality assumptions. We propose NEAT, a test for network enrichment analysis. The test is based on the hypergeometric distribution, which naturally arises as the null distribution in this context. NEAT can be applied not only to undirected, but to directed and partially directed networks as well. Our simulations indicate that NEAT is considerably faster than alternative resampling-based methods, and that its capacity to detect enrichments is at least as good as the one of alternative tests. We discuss applications of NEAT to network analyses in yeast by testing for enrichment of the Environmental Stress Response target gene set with GO Slim and KEGG functional gene sets, and also by inspecting associations between functional sets themselves. NEAT is a flexible and efficient test for network enrichment analysis that aims to overcome some limitations of existing resampling-based tests. The method is implemented in the R package neat, which can be freely downloaded from CRAN ( https://cran.r-project.org/package=neat ).

  3. Methods in Symbolic Computation and p-Adic Valuations of Polynomials

    NASA Astrophysics Data System (ADS)

    Guan, Xiao

    Symbolic computation has widely appear in many mathematical fields such as combinatorics, number theory and stochastic processes. The techniques created in the area of experimental mathematics provide us efficient ways of symbolic computing and verification of complicated relations. Part I consists of three problems. The first one focuses on a unimodal sequence derived from a quartic integral. Many of its properties are explored with the help of hypergeometric representations and automatic proofs. The second problem tackles the generating function of the reciprocal of Catalan number. It springs from the closed form given by Mathematica. Furthermore, three methods in special functions are used to justify this result. The third issue addresses the closed form solutions for the moments of products of generalized elliptic integrals , which combines the experimental mathematics and classical analysis. Part II concentrates on the p-adic valuations of polynomials from the perspective of trees. For a given polynomial f( n) indexed in positive integers, the package developed in Mathematica will create certain tree structure following a couple of rules. The evolution of such trees are studied both rigorously and experimentally from the view of field extension, nonparametric statistics and random matrix.

  4. Inverse curvature flows in asymptotically Robertson Walker spaces

    NASA Astrophysics Data System (ADS)

    Kröner, Heiko

    2018-04-01

    In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.

  5. Numerical solution of Euler's equation by perturbed functionals

    NASA Technical Reports Server (NTRS)

    Dey, S. K.

    1985-01-01

    A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

  6. Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

    NASA Astrophysics Data System (ADS)

    Ormerod, Christopher M.

    2014-01-01

    We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

  7. Image segmentation using hidden Markov Gauss mixture models.

    PubMed

    Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M

    2007-07-01

    Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

  8. Controllable light capsules employing modified Bessel-Gauss beams

    PubMed Central

    Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei

    2016-01-01

    We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms. PMID:27388558

  9. Evaluating secular acceleration in geomagnetic field model GRIMM-3

    NASA Astrophysics Data System (ADS)

    Lesur, V.; Wardinski, I.

    2012-12-01

    Secular acceleration of the magnetic field is the rate of change of its secular variation. One of the main results of studying magnetic data collected by the German survey satellite CHAMP was the mapping of field acceleration and its evolution in time. Questions remain about the accuracy of the modeled acceleration and the effect of the applied regularization processes. We have evaluated to what extent the regularization affects the temporal variability of the Gauss coefficients. We also obtained results of temporal variability of the Gauss coefficients where alternative approaches to the usual smoothing norms have been applied for regularization. Except for the dipole term, the secular acceleration of the Gauss coefficients is fairly well described up to spherical harmonic degree 5 or 6. There is no clear evidence from observatory data that the spectrum of this acceleration is underestimated at the Earth surface. Assuming a resistive mantle, the observed acceleration supports a characteristic time scale for the secular variation of the order of 11 years.

  10. Competing s-wave orders from Einstein-Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Li, Zhi-Hong; Fu, Yun-Chang; Nie, Zhang-Yu

    2018-01-01

    In this paper, the holographic superconductor model with two s-wave orders from 4 + 1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe limit. At different values of the Gauss-Bonnet coefficient α, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s + s coexistent phase, including the reentrant phase transition near the Chern-Simons limit α = 0.25, can be found. We also give an explanation to the nontrivial behavior of the Tc- α curves near the Chern-Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern-Simons limit.

  11. Euler-Lagrange formulas for pseudo-Kähler manifolds

    NASA Astrophysics Data System (ADS)

    Park, JeongHyeong

    2016-01-01

    Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m > 2 k. Taking the inner product with the Kähler form Ωk gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler-Lagrange equations are a generalized Einstein-Gauss-Bonnet gravity theory; this theory restricts to the canonical formalism if c =c2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting.

  12. Causal structures in Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Izumi, Keisuke

    2014-08-01

    We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the "event horizon" in the sense of causality. We also analyze causal structures on nonstationary solutions with (D-2)-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, RABNANB≥0 for any null vector NA, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the "black hole" defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.

  13. Solving radiative transfer with line overlaps using Gauss-Seidel algorithms

    NASA Astrophysics Data System (ADS)

    Daniel, F.; Cernicharo, J.

    2008-09-01

    Context: The improvement in observational facilities requires refining the modelling of the geometrical structures of astrophysical objects. Nevertheless, for complex problems such as line overlap in molecules showing hyperfine structure, a detailed analysis still requires a large amount of computing time and thus, misinterpretation cannot be dismissed due to an undersampling of the whole space of parameters. Aims: We extend the discussion of the implementation of the Gauss-Seidel algorithm in spherical geometry and include the case of hyperfine line overlap. Methods: We first review the basics of the short characteristics method that is used to solve the radiative transfer equations. Details are given on the determination of the Lambda operator in spherical geometry. The Gauss-Seidel algorithm is then described and, by analogy to the plan-parallel case, we see how to introduce it in spherical geometry. Doing so requires some approximations in order to keep the algorithm competitive. Finally, line overlap effects are included. Results: The convergence speed of the algorithm is compared to the usual Jacobi iterative schemes. The gain in the number of iterations is typically factors of 2 and 4 for the two implementations made of the Gauss-Seidel algorithm. This is obtained despite the introduction of approximations in the algorithm. A comparison of results obtained with and without line overlaps for N2H^+, HCN, and HNC shows that the J=3-2 line intensities are significantly underestimated in models where line overlap is neglected.

  14. Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Keratoconus Eyes after Accelerated Corneal Collagen Crosslinking

    PubMed Central

    Caravaca-Arens, Esteban; de Fez, Dolores; Blanes-Mompó, Francisco J.

    2017-01-01

    Purpose To analyze the errors associated to corneal power calculation using the keratometric approach in keratoconus eyes after accelerated corneal collagen crosslinking (CXL) surgery and to obtain a model for the estimation of an adjusted corneal refractive index (nkadj) minimizing such errors. Methods Potential differences (ΔPc) among keratometric (Pk) and Gaussian corneal power (PcGauss) were simulated. Three algorithms based on the use of nkadj for the estimation of an adjusted keratometric corneal power (Pkadj) were developed. The agreement between Pk(1.3375) (keratometric power using the keratometric index of 1.3375), PcGauss, and Pkadj was evaluated. The validity of the algorithm developed was investigated in 21 keratoconus eyes undergoing accelerated CXL. Results P k(1.3375) overestimated corneal power between 0.3 and 3.2 D in theoretical simulations and between 0.8 and 2.9 D in the clinical study (ΔPc). Three linear equations were defined for nkadj to be used for different ranges of r1c. In the clinical study, differences between Pkadj and PcGauss did not exceed ±0.8 D nk = 1.3375. No statistically significant differences were found between Pkadj and PcGauss (p > 0.05) and Pk(1.3375) and Pkadj (p < 0.001). Conclusions The use of the keratometric approach in keratoconus eyes after accelerated CXL can lead to significant clinical errors. These errors can be minimized with an adjusted keratometric approach. PMID:29201459

  15. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Choun, Yoon Seok, E-mail: ychoun@gmail.com

    The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric {sub 2}F{sub 1}, {sub 1}F{sub 1} and {sub 0}F{sub 1} functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A{sub n}’s. Section 3 contains my analysismore » on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B{sub n} term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries.« less

  16. Geometry of the submanifolds of SEXn. II. The generalized fundamental equations for the hypersubmanifold of SEXn

    NASA Astrophysics Data System (ADS)

    Chung, Kyung Tae; Lee, Jong Woo

    1989-08-01

    A connection which is both Einstein and semisymmetric is called an SE connection, and a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by g λμ through an SE connection is called an n-dimensional SE manifold and denoted by SEXn. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEXn, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.

  17. A Multilevel Approach to the Algebraic Image Reconstruction Problem

    DTIC Science & Technology

    1994-06-01

    and later use this fact to show that the Gauss-Seidel method when applied to the problem cannot diverge and in fact must converge. Theorem 4.2: B is...First, we show that the Gauss-Seidel method cannot diverge for this problem. We introduce the following definitions: 71 Definition 5.1: The energy...Seidel cannot diverge . Recall that (5.4) is ~k+l) - _2_ (b·- ~ .. (k+l) - ~ .. (k)) x~ - , L......t q,1 x 1 L......t a,1 x 1 , qii j=l j=i+l 1 ~ i

  18. Magnetic Design Guidelines for Electronic Power Supplies.

    DTIC Science & Technology

    1986-09-30

    henries ",= peak flux density in gauss d = wire (conductor) dia in mils CM = d2 = circular mi’s Irms = RMS current in amperes Idc = DC current in...component lac = RMS ac current in the inductor f = minimum frequency in hertz L = inductance in henries Then Eac 2 16.83 x 2, x 760 x .05 10 Eac 1 168.3 x 2...duty cycle x 1/f L inductance in henries *permeability in gauss/oersted H magnetizing force in oersteds ’. i g length of air gap in cm ic length of

  19. On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

    NASA Astrophysics Data System (ADS)

    Ernazarov, K. K.

    2017-12-01

    We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

  20. Iterative methods used in overlap astrometric reduction techniques do not always converge

    NASA Astrophysics Data System (ADS)

    Rapaport, M.; Ducourant, C.; Colin, J.; Le Campion, J. F.

    1993-04-01

    In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurring in overlapping reduction methods of astrometry do not always converge. We exhibit examples of divergence. We then analyze an alternative algorithm proposed by Wang (1985). We prove the consistency of this algorithm and verify that it can be convergent while the Gauss-Seidel method is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.

  1. A comparison theorem for the SOR iterative method

    NASA Astrophysics Data System (ADS)

    Sun, Li-Ying

    2005-09-01

    In 1997, Kohno et al. have reported numerically that the improving modified Gauss-Seidel method, which was referred to as the IMGS method, is superior to the SOR iterative method. In this paper, we prove that the spectral radius of the IMGS method is smaller than that of the SOR method and Gauss-Seidel method, if the relaxation parameter [omega][set membership, variant](0,1]. As a result, we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods. Some recent results are improved.

  2. A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Cattaneo, Alberto S.; Perez, Alejandro

    2017-05-01

    We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

  3. Gauss's law test of gravity at short range

    NASA Technical Reports Server (NTRS)

    Moody, M. V.; Paik, H. J.

    1993-01-01

    A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2-sigma) limit of alpha = (0.9 + or - 4.6) x 10 exp -4 at lambda of 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(l + alpha e exp -r/lambda).

  4. Dataset for petroleum based stock markets and GAUSS codes for SAMEM.

    PubMed

    Khalifa, Ahmed A A; Bertuccelli, Pietro; Otranto, Edoardo

    2017-02-01

    This article includes a unique data set of a balanced daily (Monday, Tuesday and Wednesday) for oil and natural gas volatility and the oil rich economies' stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006-July 30, 2015. Additionally, we have included unique GAUSS codes for estimating the spillover asymmetric multiplicative error model (SAMEM) with application to Petroleum-Based Stock Market. The data, the model and the codes have many applications in business and social science.

  5. Cartesian and polar Schmidt bases for down-converted photons. How high dimensional entanglement protects the shared information from non-ideal measurements

    NASA Astrophysics Data System (ADS)

    Miatto, F. M.; Brougham, T.; Yao, A. M.

    2012-07-01

    We derive an analytical form of the Schmidt modes of spontaneous parametric down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We show that these correspond to Hermite-Gauss (HG) or Laguerre-Gauss (LG) modes only for a specific value of their width, and we show how such value depends on the experimental parameters. The Schmidt modes that we explicitly derive allow one to set up an optimised projection basis that maximises the mutual information gained from a joint measurement. The possibility of doing so with LG modes makes it possible to take advantage of the properties of orbital angular momentum eigenmodes. We derive a general entropic entanglement measure using the Rényi entropy as a function of the Schmidt number, K, and then retrieve the von Neumann entropy, S. Using the relation between S and K we show that, for highly entangled states, a non-ideal measurement basis does not degrade the number of shared bits by a large extent. More specifically, given a non-ideal measurement which corresponds to the loss of a fraction of the total number of modes, we can quantify the experimental parameters needed to generate an entangled SPDC state with a sufficiently high dimensionality to retain any given fraction of shared bits.

  6. A Gaussian quadrature method for total energy analysis in electronic state calculations

    NASA Astrophysics Data System (ADS)

    Fukushima, Kimichika

    This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.

  7. Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    1997-01-01

    This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

  8. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Stimpson, Shane; Collins, Benjamin; Kochunas, Brendan

    The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2Dmore » method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$-$as is the case with the Gauss-Seidel sweeper$-$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8$-$10% increase in the overall memory requirement.« less

  9. Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

    DOE PAGES

    Stimpson, Shane; Collins, Benjamin; Kochunas, Brendan

    2017-03-10

    The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2Dmore » method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$-$as is the case with the Gauss-Seidel sweeper$-$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8$-$10% increase in the overall memory requirement.« less

  10. General aspects of Gauss-Bonnet models without potential in dimension four

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com

    In the present work, the isotropic and homogenous solutions with spatial curvature k =0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]–[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=( H (φ), φ) which is the solution of a polynomial equation P ( H {sup 2}, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on themore » evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f (φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point φ-dot →0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H → 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]–[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future.« less

  11. Utah State University Global Assimilation of Ionospheric Measurements Gauss-Markov Kalman filter model of the ionosphere: Model description and validation

    NASA Astrophysics Data System (ADS)

    Scherliess, L.; Schunk, R. W.; Sojka, J. J.; Thompson, D. C.; Zhu, L.

    2006-11-01

    The Utah State University Gauss-Markov Kalman Filter (GMKF) was developed as part of the Global Assimilation of Ionospheric Measurements (GAIM) program. The GMKF uses a physics-based model of the ionosphere and a Gauss-Markov Kalman filter as a basis for assimilating a diverse set of real-time (or near real-time) observations. The physics-based model is the Ionospheric Forecast Model (IFM), which accounts for five ion species and covers the E region, F region, and the topside from 90 to 1400 km altitude. Within the GMKF, the IFM derived ionospheric densities constitute a background density field on which perturbations are superimposed based on the available data and their errors. In the current configuration, the GMKF assimilates slant total electron content (TEC) from a variable number of global positioning satellite (GPS) ground sites, bottomside electron density (Ne) profiles from a variable number of ionosondes, in situ Ne from four Defense Meteorological Satellite Program (DMSP) satellites, and nighttime line-of-sight ultraviolet (UV) radiances measured by satellites. To test the GMKF for real-time operations and to validate its ionospheric density specifications, we have tested the model performance for a variety of geophysical conditions. During these model runs various combination of data types and data quantities were assimilated. To simulate real-time operations, the model ran continuously and automatically and produced three-dimensional global electron density distributions in 15 min increments. In this paper we will describe the Gauss-Markov Kalman filter model and present results of our validation study, with an emphasis on comparisons with independent observations.

  12. Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

    NASA Astrophysics Data System (ADS)

    Wei, Shao-Wen; Liu, Yu-Xiao

    2014-08-01

    We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in d-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state T=T(v,P), we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the T-v (T-rh) line with fixed pressure P. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge Q and dimension d. The result shows that the small/large black hole phase transitions appear for any d, which is reminiscent of the liquid/gas transition of a Van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for d=6 and Q ∈(0.1705,0.1946).

  13. Imaging of trabecular meshwork using Bessel-Gauss light sheet with fluorescence

    NASA Astrophysics Data System (ADS)

    Jie Jeesmond Hong, Xun; Shinoj, V. K.; Murukeshan, V. M.; Baskaran, M.; Aung, Tin

    2017-03-01

    Ocular imaging technology that holds promise for both fundamental investigation and clinical detection of glaucoma is still a challenging research area. A direct view of the trabecular meshwork (TM) with high resolution is not generally possible because the iridocorneal angle region is obstructed by the sclera overlap. The best approach to observe the aqueous outflow system (AOS) is therefore to view from the opposite angle. In this research work, we developed two imaging systems for the high resolution ex vivo studies of the AOS inside porcine eye, based on a Gaussian illuminated and a digitally scanned Bessel-Gauss beam light sheet fluorescence configurations. The digitally scanned Bessel-Gauss beam is able to overcome the trade-off between the length and thickness of the Gaussian light sheet to give better imaging performance. It has adequate spatial resolution to resolve critical anatomical structures such as the TM, thereby enabling objective information about the AOS. This non-contact and non-invasive imaging methodology with excellent safety profile is expected to be well received by vision researchers and clinicians in the evaluation and management of glaucoma.

  14. Comparison of Nonequilibrium Solution Algorithms Applied to Chemically Stiff Hypersonic Flows

    NASA Technical Reports Server (NTRS)

    Palmer, Grant; Venkatapathy, Ethiraj

    1995-01-01

    Three solution algorithms, explicit under-relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in its descent trajectory. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness.The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15 and 30, the lower-upper symmetric Gauss-Seidel method produces an eight order of magnitude drop in the energy residual in one-third to one-half the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 30 and above. At Mach 40 the performance of the lower-upper symmetric Gauss-Seidel algorithm deteriorates to the point that it is out performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

  15. Millisecond radio spikes from the dwarf M flare star AD Leonis

    NASA Technical Reports Server (NTRS)

    Lang, K. R.; Willson, R. F.

    1986-01-01

    Arecibo radio observations of millisec bursts of radio signals at 1415 MHz from AD Leonis are reported. The observed burst had an ellipticity of 0.95, 50-100 percent circular polarization, and a flux density maximum of 30 mJy. The 50 sec burst featured five quasi-periodic oscillations with a mean periodicity of about 3.2 sec. A second, less intense burst that occurred 20 sec later was 100 percent circularly polarized. The area emitting the bursts covered an estimated 0.005 of the radius of AD Leonis and had an electron density of 6 billion/cu cm and a longitudinal magnetic field strength of 250 gauss, if the source was an electron-cyclotron maser. A coherent plasma source would require, for the first harmonic, an electron density of 20 billion/cu cm and a magnetic field much less than 500 gauss. A second harmonic of the plasma frequency would require an electron density of 6 billion/cu cm and a field strength much less than 250 gauss. The possibility that the source was periodic oscillations in coronal loops is discussed.

  16. Charge-to-mass dispersion methods for abrasion-ablation fragmentation models

    NASA Technical Reports Server (NTRS)

    Townsend, L. W.; Norbury, J. W.

    1985-01-01

    Methods to describe the charge-to-mass dispersion distributions of projectile prefragments are presented and used to determine individual isotope cross-sections or various elements produced in the fragmentation of relativistic argon nuclei by carbon targets. Although slight improvements in predicted cross-sections are obtained for the quantum mechanical giant dipole resonance (GDR) distribution when compared qith the predictions of the geometric GDR model, the closest agreement between theory and experiment continues to be obtained with the simple hypergeometric distribution, which treats the nucleons in the nucleus as completely uncorrelated.

  17. Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

    PubMed

    Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

    2014-06-10

    The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

  18. Tensor products of U{sub q}{sup Prime }sl-caret(2)-modules and the big q{sup 2}-Jacobi function transform

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gade, R. M.

    2013-01-15

    Four tensor products of evaluation modules of the quantum affine algebra U{sub q}{sup Prime }sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} and {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} involving big q{sup 2}-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplestmore » sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q{sup 2}-Jacobi function transform pair. An integral decomposition is obtained for the sum {tau}{sup (r,t)}. A partial description of the relation between the decompositions of the tensor products with respect to U{sub q}sl(2) or with respect to its complement in U{sub q}{sup Prime }sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U{sub q}{sup Prime }sl-caret(2)-submodules is discussed.« less

  19. Noether symmetry approach in f(G,T) gravity

    NASA Astrophysics Data System (ADS)

    Shamir, M. Farasat; Ahmad, Mushtaq

    2017-01-01

    We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f(G,T) pragmatic with G, the Gauss-Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f(G,T) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f(G,T) gravity model.

  20. A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

    NASA Technical Reports Server (NTRS)

    Carpenter, Russell; Lee, Taesul

    2008-01-01

    Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

  1. Ince-gauss based multiple intermodal phase-matched third-harmonic generations in a step-index silica optical fiber

    NASA Astrophysics Data System (ADS)

    Borne, Adrien; Katsura, Tomotaka; Félix, Corinne; Doppagne, Benjamin; Segonds, Patricia; Bencheikh, Kamel; Levenson, Juan Ariel; Boulanger, Benoit

    2016-01-01

    Several third-harmonic generation processes were performed in a single step-index germanium-doped silica optical fiber under intermodal phase-matching conditions. The nanosecond fundamental beam range between 1400 and 1600 nm. The transverse distributions of the energy were successfully modeled in the form of Ince-Gauss modes, pointing out some ellipticity of fiber core. From these experiments and theoretical calculations, we discuss the implementation of frequency degenerated triple photon generation that shares the same phase-matching condition as third-harmonic generation, which is its reverse process.

  2. Iterative algorithm for reconstructing rotationally asymmetric surface deviation with pixel-level spatial resolution

    NASA Astrophysics Data System (ADS)

    Quan, Haiyang; Wu, Fan; Hou, Xi

    2015-10-01

    New method for reconstructing rotationally asymmetric surface deviation with pixel-level spatial resolution is proposed. It is based on basic iterative scheme and accelerates the Gauss-Seidel method by introducing an acceleration parameter. This modified Successive Over-relaxation (SOR) is effective for solving the rotationally asymmetric components with pixel-level spatial resolution, without the usage of a fitting procedure. Compared to the Jacobi and Gauss-Seidel method, the modified SOR method with an optimal relaxation factor converges much faster and saves more computational costs and memory space without reducing accuracy. It has been proved by real experimental results.

  3. A Closely Coupled Experimental and Numerical Approach for Hypersonic and High Enthalpy Flow Investigations Utilising the HEG Shock Tunnel and the DLR TAU Code

    DTIC Science & Technology

    2010-04-01

    factorization scheme (Lower-Upper Symmetric Gauss- Seidel ) can be used for time integration. Additional convergence acceleration is achieved by the...of the full Stefan -Maxwell equations. The diffusive mass flux of species S is computed according to: for 1 for jS S S Sm j jm S j eS jd S S S j j j...approximate factorization scheme (Lower-Upper Symmetric Gauss- Seidel ). For steady state problems, equation (69) reduces to R=0 because ddU t

  4. History of the 4th Battalion, 37th Armored Regiment in Operation Desert Shield/Storm. Volume 2

    DTIC Science & Technology

    1992-04-15

    model white Toyota truck pulled into the LOGPAC area. An Arab jumped out of the driver’s side of the vehicle and grabbed a five gallon can out of the...truck bed. He looked at SGT Stephen I. Lee, the D Co supply sergeant, and asked, "Gauss? Gauss?" The Toyota truck was parked one hundred meters away...from the Toyota truck and began to happily roll an empty fifty-five gallon drum off the truck. Seeing as how I did not suffer from the same hearing

  5. Robust extraction of functional signals from gene set analysis using a generalized threshold free scoring function

    PubMed Central

    2009-01-01

    Background A central task in contemporary biosciences is the identification of biological processes showing response in genome-wide differential gene expression experiments. Two types of analysis are common. Either, one generates an ordered list based on the differential expression values of the probed genes and examines the tail areas of the list for over-representation of various functional classes. Alternatively, one monitors the average differential expression level of genes belonging to a given functional class. So far these two types of method have not been combined. Results We introduce a scoring function, Gene Set Z-score (GSZ), for the analysis of functional class over-representation that combines two previous analysis methods. GSZ encompasses popular functions such as correlation, hypergeometric test, Max-Mean and Random Sets as limiting cases. GSZ is stable against changes in class size as well as across different positions of the analysed gene list in tests with randomized data. GSZ shows the best overall performance in a detailed comparison to popular functions using artificial data. Likewise, GSZ stands out in a cross-validation of methods using split real data. A comparison of empirical p-values further shows a strong difference in favour of GSZ, which clearly reports better p-values for top classes than the other methods. Furthermore, GSZ detects relevant biological themes that are missed by the other methods. These observations also hold when comparing GSZ with popular program packages. Conclusion GSZ and improved versions of earlier methods are a useful contribution to the analysis of differential gene expression. The methods and supplementary material are available from the website http://ekhidna.biocenter.helsinki.fi/users/petri/public/GSZ/GSZscore.html. PMID:19775443

  6. Cosmological magnetic fields as string dynamo seeds and axion fields in torsioned spacetime

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    De Andrade, L.C. Garcia, E-mail: garcia@dft.if.uerj.br

    2014-08-01

    In this paper two examples of the generation cosmological magnetic fields (CMF) are given. The first is the string dynamo seed cosmological magnetic field estimated as B{sub seed}∼10{sup -24} Gauss from a static spin polarised cylinder in Einstein-Cartan-Maxwell spacetime. The string dynamo seeds from a static spin polarised cylinder is given by B∼σ{sup 2}R{sup 2} where σ is the spin-torsion density while R is the string radius. The B-field value above is able to seed galactic dynamo. In the BBN the magnetic fields around 10{sup 12} Gauss give rise to a string radius as small as 10{sup 17}l{sub P} where l{sub P}more » is the Planck length. The second is the CMF from axionic torsion field which is given by B{sub seed}∼10{sup -27} Gauss which is stronger than the primordial magnetic field B{sub BICEP2}∼10{sup -30} Gauss from the BICEP2 recent experiment on primordial gravitational waves and cosmological inflation to axionic torsion. The interaction Lagrangean between axionic torsion scalar φ and magnetic fields used in this last example is given by f{sup 2}(φ)F{sub μν}F{sup μν}. A similar lagrangean has been used by K. Bamba et al. [JCAP 10 (2012) 058] so generate magnetic fields without dynamo action. Since axionic torsion can be associated with axionic domain walls both examples discussed here could be consider as topological defects examples of the generation of primordial magnetic fields in universes endowed with spacetime torsion.« less

  7. Parallelization of Lower-Upper Symmetric Gauss-Seidel Method for Chemically Reacting Flow

    NASA Technical Reports Server (NTRS)

    Yoon, Seokkwan; Jost, Gabriele; Chang, Sherry

    2005-01-01

    Development of technologies for exploration of the solar system has revived an interest in computational simulation of chemically reacting flows since planetary probe vehicles exhibit non-equilibrium phenomena during the atmospheric entry of a planet or a moon as well as the reentry to the Earth. Stability in combustion is essential for new propulsion systems. Numerical solution of real-gas flows often increases computational work by an order-of-magnitude compared to perfect gas flow partly because of the increased complexity of equations to solve. Recently, as part of Project Columbia, NASA has integrated a cluster of interconnected SGI Altix systems to provide a ten-fold increase in current supercomputing capacity that includes an SGI Origin system. Both the new and existing machines are based on cache coherent non-uniform memory access architecture. Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation method has been implemented into both perfect and real gas flow codes including Real-Gas Aerodynamic Simulator (RGAS). However, the vectorized RGAS code runs inefficiently on cache-based shared-memory machines such as SGI system. Parallelization of a Gauss-Seidel method is nontrivial due to its sequential nature. The LU-SGS method has been vectorized on an oblique plane in INS3D-LU code that has been one of the base codes for NAS Parallel benchmarks. The oblique plane has been called a hyperplane by computer scientists. It is straightforward to parallelize a Gauss-Seidel method by partitioning the hyperplanes once they are formed. Another way of parallelization is to schedule processors like a pipeline using software. Both hyperplane and pipeline methods have been implemented using openMP directives. The present paper reports the performance of the parallelized RGAS code on SGI Origin and Altix systems.

  8. Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power in normal eyes.

    PubMed

    Piñero, David P; Camps, Vicente J; Mateo, Verónica; Ruiz-Fortes, Pedro

    2012-08-01

    To validate clinically in a normal healthy population an algorithm to correct the error in the keratometric estimation of corneal power based on the use of a variable keratometric index of refraction (n(k)). Medimar International Hospital (Oftalmar) and University of Alicante, Alicante, Spain. Case series. Corneal power was measured with a Scheimpflug photography-based system (Pentacam software version 1.14r01) in healthy eyes with no previous ocular surgery. In all cases, keratometric corneal power was also estimated using an adjusted value of n(k) that is dependent on the anterior corneal radius (r(1c)) as follows: n(kadj) = -0.0064286 r(1c) +1.37688. Agreement between the Gaussian (P(c)(Gauss)) and adjusted keratometric (P(kadj)) corneal power values was evaluated. The study evaluated 92 eyes (92 patients; age range 15 to 64 years). The mean difference between P(c)(Gauss) and P(kadj) was -0.02 diopter (D) ± 0.22 (SD) (P=.43). A very strong, statistically significant correlation was found between both corneal powers (r = .994, P<.01). The range of agreement between P(c)(Gauss) and P(kadj) was 0.44 D, with limits of agreement of -0.46 and +0.42 D. In addition, a very strong, statistically significant correlation of the difference between P(c)(Gauss) and P(kadj) and the posterior corneal radius was found (r = 0.96, P<.01). The imprecision in the calculation of corneal power using keratometric estimation can be minimized in clinical practice by using a variable keratometric index that depends on the radius of the anterior corneal surface. No author has a financial or proprietary interest in any material or method mentioned. Copyright © 2012 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.

  9. Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Keratoconus Eyes after Accelerated Corneal Collagen Crosslinking.

    PubMed

    Piñero, David P; Camps, Vicente J; Caravaca-Arens, Esteban; de Fez, Dolores; Blanes-Mompó, Francisco J

    2017-01-01

    To analyze the errors associated to corneal power calculation using the keratometric approach in keratoconus eyes after accelerated corneal collagen crosslinking (CXL) surgery and to obtain a model for the estimation of an adjusted corneal refractive index ( n k adj ) minimizing such errors. Potential differences (Δ P c ) among keratometric ( P k ) and Gaussian corneal power ( P c Gauss ) were simulated. Three algorithms based on the use of n k adj for the estimation of an adjusted keratometric corneal power ( P k adj ) were developed. The agreement between P k (1.3375) (keratometric power using the keratometric index of 1.3375), P c Gauss , and P k adj was evaluated. The validity of the algorithm developed was investigated in 21 keratoconus eyes undergoing accelerated CXL. P k (1.3375) overestimated corneal power between 0.3 and 3.2 D in theoretical simulations and between 0.8 and 2.9 D in the clinical study (Δ P c ). Three linear equations were defined for n k adj to be used for different ranges of r 1c . In the clinical study, differences between P k adj and P c Gauss did not exceed ±0.8 D n k = 1.3375. No statistically significant differences were found between P k adj and P c Gauss ( p > 0.05) and P k (1.3375) and P k adj ( p < 0.001). The use of the keratometric approach in keratoconus eyes after accelerated CXL can lead to significant clinical errors. These errors can be minimized with an adjusted keratometric approach.

  10. PubMed Phrases, an open set of coherent phrases for searching biomedical literature

    PubMed Central

    Kim, Sun; Yeganova, Lana; Comeau, Donald C.; Wilbur, W. John; Lu, Zhiyong

    2018-01-01

    In biomedicine, key concepts are often expressed by multiple words (e.g., ‘zinc finger protein’). Previous work has shown treating a sequence of words as a meaningful unit, where applicable, is not only important for human understanding but also beneficial for automatic information seeking. Here we present a collection of PubMed® Phrases that are beneficial for information retrieval and human comprehension. We define these phrases as coherent chunks that are logically connected. To collect the phrase set, we apply the hypergeometric test to detect segments of consecutive terms that are likely to appear together in PubMed. These text segments are then filtered using the BM25 ranking function to ensure that they are beneficial from an information retrieval perspective. Thus, we obtain a set of 705,915 PubMed Phrases. We evaluate the quality of the set by investigating PubMed user click data and manually annotating a sample of 500 randomly selected noun phrases. We also analyze and discuss the usage of these PubMed Phrases in literature search. PMID:29893755

  11. Cosmological constraints and comparison of viable f (R ) models

    NASA Astrophysics Data System (ADS)

    Pérez-Romero, Judit; Nesseris, Savvas

    2018-01-01

    In this paper we present cosmological constraints on several well-known f (R ) models, but also on a new class of models that are variants of the Hu-Sawicki one of the form f (R )=R -2/Λ 1 +b y (R ,Λ ) , that interpolate between the cosmological constant model and a matter dominated universe for different values of the parameter b , which is usually expected to be small for viable models and which in practice measures the deviation from general relativity. We use the latest growth rate, cosmic microwave background, baryon acoustic oscillations, supernovae type Ia and Hubble parameter data to place stringent constraints on the models and to compare them to the cosmological constant model but also other viable f (R ) models such as the Starobinsky or the degenerate hypergeometric models. We find that these kinds of Hu-Sawicki variant parametrizations are in general compatible with the currently available data and can provide useful toy models to explore the available functional space of f (R ) models, something very useful with the current and upcoming surveys that will test deviations from general relativity.

  12. Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis

    NASA Astrophysics Data System (ADS)

    Di Cristo, Cristiana; Iervolino, Michele; Vacca, Andrea

    2018-04-01

    The paper investigates the applicability of Kinematic and Diffusive Wave models for mud-flows with a power-law shear-thinning rheology. In analogy with a well-known approach for turbulent clear-water flows, the study compares the steady flow depth profiles predicted by approximated models with those of the Full Dynamic Wave one. For all the models and assuming an infinitely wide channel, the analytical solution of the flow depth profiles, in terms of hypergeometric functions, is derived. The accuracy of the approximated models is assessed by computing the average, along the channel length, of the errors, for several values of the Froude and kinematic wave numbers. Assuming the threshold value of the error equal to 5%, the applicability conditions of the two approximations have been individuated for several values of the power-law exponent, showing a crucial role of the rheology. The comparison with the clear-water results indicates that applicability criteria for clear-water flows do not apply to shear-thinning fluids, potentially leading to an incorrect use of approximated models if the rheology is not properly accounted for.

  13. Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

    NASA Astrophysics Data System (ADS)

    Miller, W., Jr.; Li, Q.

    2015-04-01

    The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

  14. Block-circulant matrices with circulant blocks, Weil sums, and mutually unbiased bases. II. The prime power case

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Combescure, Monique

    2009-03-15

    In our previous paper [Combescure, M., 'Circulant matrices, Gauss sums and the mutually unbiased bases. I. The prime number case', Cubo A Mathematical Journal (unpublished)] we have shown that the theory of circulant matrices allows to recover the result that there exists p+1 mutually unbiased bases in dimension p, p being an arbitrary prime number. Two orthonormal bases B, B{sup '} of C{sup d} are said mutually unbiased if for all b(set-membership sign)B, for all b{sup '}(set-membership sign)B{sup '} one has that |b{center_dot}b{sup '}|=1/{radical}(d) (b{center_dot}b{sup '} Hermitian scalar product in C{sup d}). In this paper we show that the theorymore » of block-circulant matrices with circulant blocks allows to show very simply the known result that if d=p{sup n} (p a prime number and n any integer) there exists d+1 mutually unbiased bases in C{sup d}. Our result relies heavily on an idea of Klimov et al. [''Geometrical approach to the discrete Wigner function,'' J. Phys. A 39, 14471 (2006)]. As a subproduct we recover properties of quadratic Weil sums for p{>=}3, which generalizes the fact that in the prime case the quadratic Gauss sum properties follow from our results.« less

  15. Calculation of the angular radiance distribution for a coupled atmosphere and canopy

    NASA Technical Reports Server (NTRS)

    Liang, Shunlin; Strahler, Alan H.

    1993-01-01

    The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

  16. Mordell integrals and Giveon-Kutasov duality

    NASA Astrophysics Data System (ADS)

    Giasemidis, Georgios; Tierz, Miguel

    2016-01-01

    We solve, for finite N, the matrix model of supersymmetric U( N) Chern-Simons theory coupled to N f massive hypermultiplets of R-charge 1/2 , together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N f - 1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N f = 12 flavours).

  17. FIBER AND INTEGRAL OPTICS: Mode composition of radiation in graded-index waveguides with random microbending of the axis

    NASA Astrophysics Data System (ADS)

    Valyaev, A. B.; Krivoshlykov, S. G.

    1989-06-01

    It is shown that the problem of investigating the mode composition of a partly coherent radiation beam in a randomly inhomogeneous medium can be reduced to a study of evolution of the energy of individual modes and of the coefficients of correlations between the modes. General expressions are obtained for the coupling coefficients of modes in a parabolic waveguide with a random microbending of the axis and an analysis is made of their evolution as a function of the excitation conditions. An estimate is obtained of the distance in which a steady-state energy distribution between the modes is established. Explicit expressions are obtained for the correlation function in the case when a waveguide is excited by off-axial Gaussian beams or Gauss-Hermite modes.

  18. Detecting photons in the dark region of Laguerre-Gauss beams.

    PubMed

    Klimov, Vasily; Bloch, Daniel; Ducloy, Martial; Rios Leite, Jose R

    2009-06-08

    We show that a photon detector, sensitive to the magnetic field or to the gradient of electric field, can help to characterize the quantum properties of spatially-dependent optical fields. We discuss the excitation of an atom through magnetic dipole or electric quadrupole transitions with the photons of a Bessel beam or a Laguerre-Gauss (LG) beams. These spiral beams are shown to be not true hollow beams, due to the presence of magnetic fields and gradients of electric fields on beam axis. This approach paves the way to an analysis at the quantum level of the propagating light beams having a complicated spatial structure.

  19. Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings

    NASA Astrophysics Data System (ADS)

    Granda, L. N.; Loaiza, E.

    2016-09-01

    We study the phase space for a scalar-tensor string inspired model of dark energy with nonminimal kinetic and Gauss-Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which gives rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from a matter or radiation dominated universe to a dark energy dominated universe. Trajectories were found in the phase space departing from unstable or saddle fixed points and arriving at the stable scalar field dominated point corresponding to late-time accelerated expansion.

  20. Phantom-like behavior of a DGP-inspired Scalar-Gauss-Bonnet gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nozari, Kourosh; Azizi, Tahereh; Setare, M.R., E-mail: knozari@umz.ac.ir, E-mail: t.azizi@umz.ac.ir, E-mail: rezakord@ipm.ir

    2009-10-01

    We study the phantom-like behavior of a DGP-inspired braneworld scenario where curvature correction on the brane is taken into account. We include a possible modification of the induced gravity on the brane by incorporating higher order curvature terms of Gauss-Bonnet type. We investigate the cosmological implications of the model and we show that the normal branch of the scenario self-accelerates in this modified scenario without introducing any dark energy component. Also, a phantom-like behavior can be realized in this model without introducing any phantom field that suffers from serious difficulties such as violation of the null energy condition.

  1. Optimised collision avoidance for an ultra-close rendezvous with a failed satellite based on the Gauss pseudospectral method

    NASA Astrophysics Data System (ADS)

    Chu, Xiaoyu; Zhang, Jingrui; Lu, Shan; Zhang, Yao; Sun, Yue

    2016-11-01

    This paper presents a trajectory planning algorithm to optimise the collision avoidance of a chasing spacecraft operating in an ultra-close proximity to a failed satellite. The complex configuration and the tumbling motion of the failed satellite are considered. The two-spacecraft rendezvous dynamics are formulated based on the target body frame, and the collision avoidance constraints are detailed, particularly concerning the uncertainties. An optimisation solution of the approaching problem is generated using the Gauss pseudospectral method. A closed-loop control is used to track the optimised trajectory. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.

  2. Neutron star solutions with curvature induced scalarization in the extended Gauss-Bonnet scalar-tensor theories

    NASA Astrophysics Data System (ADS)

    Doneva, Daniela D.; Yazadjiev, Stoytcho S.

    2018-04-01

    In the present paper we study models of neutron stars in a class of extended scalar-tensor Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is exited only in the strong curvature regime. We show that in the framework of the ESTGB theories under consideration there exist new neutron star solutions which are formed via spontaneous scalarization of the general relativistic neutron stars. In contrast to the spontaneous scalarization in the standard scalar-tensor theories which is induced by the presence of matter, in our case the scalarization is induced by the spacetime curvature.

  3. On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers

    DTIC Science & Technology

    2012-08-01

    the less exact one is solved later — assigned as step 4 of Algorithm 2 — because at each iteration , the ADM updates the variables in the Gauss - Seidel ...k) and that of an accelerated version descends at O(1/k2). Then, work [14] establishes the same rates on a Gauss - Seidel version and requires only one... iteration Fig. 5.1. Convergence curves of ADM for the elastic net problem. 17 0 50 100 150 200 0.75 0.8 0.85 0.9 0.95 1 Iteration ‖u k + 1 − u ∗ ‖ 2 G / ‖u k

  4. An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Napolitano, M.; Walters, R. W.

    1985-01-01

    A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

  5. Some spectral approximation of one-dimensional fourth-order problems

    NASA Technical Reports Server (NTRS)

    Bernardi, Christine; Maday, Yvon

    1989-01-01

    Some spectral type collocation method well suited for the approximation of fourth-order systems are proposed. The model problem is the biharmonic equation, in one and two dimensions when the boundary conditions are periodic in one direction. It is proved that the standard Gauss-Lobatto nodes are not the best choice for the collocation points. Then, a new set of nodes related to some generalized Gauss type quadrature formulas is proposed. Also provided is a complete analysis of these formulas including some new issues about the asymptotic behavior of the weights and we apply these results to the analysis of the collocation method.

  6. Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

    NASA Astrophysics Data System (ADS)

    Mišković, Olivera; Olea, Rodrigo

    2011-01-01

    Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.

  7. Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

    2011-01-15

    Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, itmore » extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.« less

  8. Fracture analysis of a transversely isotropic high temperature superconductor strip based on real fundamental solutions

    NASA Astrophysics Data System (ADS)

    Gao, Zhiwen; Zhou, Youhe

    2015-04-01

    Real fundamental solution for fracture problem of transversely isotropic high temperature superconductor (HTS) strip is obtained. The superconductor E-J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Gauss-Lobatto-Chybeshev (GSL) collocation method. To guarantee a satisfactory accuracy, the convergence behavior of the kernel function is investigated. Numerical results of fracture parameters are obtained and the effects of the geometric characteristics, applied magnetic field and critical current density on the stress intensity factors (SIF) are discussed.

  9. Integrated stationary Ornstein-Uhlenbeck process, and double integral processes

    NASA Astrophysics Data System (ADS)

    Abundo, Mario; Pirozzi, Enrica

    2018-03-01

    We find a representation of the integral of the stationary Ornstein-Uhlenbeck (ISOU) process in terms of Brownian motion Bt; moreover, we show that, under certain conditions on the functions f and g , the double integral process (DIP) D(t) = ∫βt g(s) (∫αs f(u) dBu) ds can be thought as the integral of a suitable Gauss-Markov process. Some theoretical and application details are given, among them we provide a simulation formula based on that representation by which sample paths, probability densities and first passage times of the ISOU process are obtained; the first-passage times of the DIP are also studied.

  10. Transmittance and Tunneling Current through a Trapezoidal Barrier under Spin Polarization Consideration

    NASA Astrophysics Data System (ADS)

    Noor, F. A.; Nabila, E.; Mardianti, H.; Ariani, T. I.; Khairurrijal

    2018-04-01

    The transmittance and tunneling current in heterostructures under spin polarization consideration were studied by employing a zinc-blended structure for the heterostructures. An electron tunnels through a potential barrier by applying a bias voltage to the barrier, which is called the trapezoidal potential barrier. In order to study the transmittance, an Airy wave function approach was employed to find the transmittance. The obtained transmittance was then utilized to compute the tunneling current by using a Gauss quadrature method. It was shown that the transmittances were asymmetric with the incident angle of the electron. It was also shown that the tunneling currents increased as the bias voltage increased.

  11. Development of programs for computing characteristics of ultraviolet radiation

    NASA Technical Reports Server (NTRS)

    Dave, J. V.

    1972-01-01

    Efficient programs were developed for computing all four characteristics of the radiation scattered by a plane-parallel, turbid, terrestrial atmospheric model. They were developed (FORTRAN 4) and tested on the IBM /360 computers with 2314 direct access storage facility. The storage requirement varies between 200K and 750K bytes depending upon the task. The scattering phase matrix (or function) is expanded in a Fourier series whose number of terms depend upon the zenith angles of the incident and scattered radiations, as well as on the nature of aerosols. A Gauss-Seidel procedure is used for obtaining the numerical solution of the transfer equation.

  12. A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

    NASA Astrophysics Data System (ADS)

    Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

    2018-04-01

    Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

  13. Study of galactic halo F(T,TG) wormhole solutions

    NASA Astrophysics Data System (ADS)

    Sharif, M.; Nazir, Kanwal

    In this paper, we investigate static spherically symmetric wormhole solutions with galactic halo region in the background of F(T,TG) gravity. Here, T represents torsion scalar and TG is teleparallel equivalent Gauss-Bonnet term. For this purpose, we consider a diagonal tetrad and two specific F(T,TG) models. We analyze the wormhole structure through shape function graphically for both models. We also investigate the behavior of null/weak energy conditions. Finally, we evaluate the equilibrium condition to check stability of the wormhole solutions. It is concluded that there exists physically viable wormhole solution only for the first model that turns out to be stable.

  14. Computing wave functions in multichannel collisions with non-local potentials using the R-matrix method

    NASA Astrophysics Data System (ADS)

    Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena

    2017-09-01

    The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.

  15. Mood stabilizing drugs regulate transcription of immune, neuronal and metabolic pathway genes in Drosophila.

    PubMed

    Herteleer, L; Zwarts, L; Hens, K; Forero, D; Del-Favero, J; Callaerts, P

    2016-05-01

    Lithium and valproate (VPA) are drugs used in the management of bipolar disorder. Even though they reportedly act on various pathways, the transcriptional targets relevant for disease mechanism and therapeutic effect remain unclear. Furthermore, multiple studies used lymphoblasts of bipolar patients as a cellular proxy, but it remains unclear whether peripheral cells provide a good readout for the effects of these drugs in the brain. We used Drosophila culture cells and adult flies to analyze the transcriptional effects of lithium and VPA and define mechanistic pathways. Transcriptional profiles were determined for Drosophila S2-cells and adult fly heads following lithium or VPA treatment. Gene ontology categories were identified using the DAVID functional annotation tool with a cut-off of p < 0.05. Significantly enriched GO terms were clustered using REVIGO and DAVID functional annotation clustering. Significance of overlap between transcript lists was determined with a Fisher's exact hypergeometric test. Treatment of cultured cells and adult flies with lithium and VPA induces transcriptional responses in genes with similar ontology, with as most prominent immune response, neuronal development, neuronal function, and metabolism. (i) Transcriptional effects of lithium and VPA in Drosophila S2 cells and heads show significant overlap. (ii) The overlap between transcriptional alterations in peripheral versus neuronal cells at the single gene level is negligible, but at the gene ontology and pathway level considerable overlap can be found. (iii) Lithium and VPA act on evolutionarily conserved pathways in Drosophila and mammalian models.

  16. - XSUMMER- Transcendental functions and symbolic summation in FORM

    NASA Astrophysics Data System (ADS)

    Moch, S.; Uwer, P.

    2006-05-01

    Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system FORM. Program summaryTitle of program:XSUMMER Catalogue identifier:ADXQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0 Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland License:GNU Public License and FORM License Computers:all Operating system:all Program language:FORM Memory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAM No. of lines in distributed program, including test data, etc.:9854 No. of bytes in distributed program, including test data, etc.:126 551 Distribution format:tar.gz Other programs called:none External files needed:none Nature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory. Method of solution:Algebraic manipulations of nested sums. Restrictions on complexity of the problem:Usually limited only by the available disk space. Typical running time:Dependent on the complexity of the problem.

  17. The Green's functions for peridynamic non-local diffusion.

    PubMed

    Wang, L J; Xu, J F; Wang, J X

    2016-09-01

    In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

  18. Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

    NASA Astrophysics Data System (ADS)

    Crisnejo, Gabriel; Gallo, Emanuel

    2018-06-01

    We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.

  19. Optimization experiments with a double Gauss lens

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brixner, B.; Klein, M.M.

    1988-05-01

    This paper describes how a lens can be generated by starting from plane surfaces. Three different experiments, using the Los Alamos National Laboratory optimization procedure, all converged on the same stable prescriptions in the optimum minimum region. The starts were made first from an already optimized lens appearing in the literature, then from a powerless plane-surfaces configuration, and finally from a crude Super Angulon configuration. In each case the result was a double Gauss lens, which suggests that this type of lens may be the best compact six-glass solution for one imaging problem: an f/2 aperture and a moderate fieldmore » of view. The procedures and results are discussed in detail.« less

  20. Optimization Experiments With A Double Gauss Lens

    NASA Astrophysics Data System (ADS)

    Brixner, Berlyn; Klein, Morris M.

    1988-05-01

    This paper describes how a lens can be generated by starting from plane surfaces. Three different experiments, using the Los Alamos National Laboratory optimization procedure, all converged on the same stable prescriptions in the optimum minimum region. The starts were made first from an already optimized lens appearing in the literature, then from a powerless plane-surfaces configuration, and finally from a crude Super Angulon configuration. In each case the result was a double Gauss lens, which suggests that this type of lens may be the best compact six-glass solution for one imaging problem: an f/2 aperture and a moderate field of view. The procedures and results are discussed in detail.

  1. Polarimetry and spectroscopy of a simple sunspot. I - On the magnetic field of a sunspot penumbra

    NASA Technical Reports Server (NTRS)

    Schmidt, W.; Hofmann, A.; Balthasar, H.; Tarbell, T. D.; Frank, Z. A.

    1992-01-01

    We investigate the magnetic field structure of a medium sized sunspot using high resolution magnetograms and spectrograms and derive a relationship between the brightness of penumbral structures and the inclination of the magnetic field. The field inclination to the spot normal is larger in the dark structures than in the bright ones. We show that the field strength does not vary between dark and bright structures. At the inner penumbral boundary the field strength is 2000 Gauss and about 1000 Gauss at the outer penumbral edge. The line-of sight component of the material flow decreases rapidly within one arcsecond at the photospheric boundary of the spot.

  2. Cosmic backreaction and Gauss's law

    NASA Astrophysics Data System (ADS)

    Fleury, Pierre

    2017-06-01

    Cosmic backreaction refers to the general question of whether a homogeneous and isotropic cosmological model is able to predict the correct expansion dynamics of our inhomogeneous Universe. One aspect of this issue concerns the validity of the continuous approximation: does a system of point masses expand the same way as a fluid does? This article shows that it is not exactly the case in Newtonian gravity, although the associated corrections vanish in an infinite Universe. It turns out that Gauss's law is a key ingredient for such corrections to vanish. Backreaction, therefore, generically arises in alternative theories of gravitation, which threatens the trustworthiness of their cosmological tests. This phenomenon is illustrated with a toy model of massive gravity.

  3. On stable exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

    NASA Astrophysics Data System (ADS)

    Ivashchuk, V. D.; Ernazarov, K. K.

    2017-01-01

    A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ˜ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.

  4. The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Spence, Peter J., E-mail: peter.spence@awe.co.uk

    A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadraturemore » sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent, with the highest order tabulated sets showing unexpected anomalies. Although not in an actual transport setting, the accuracy of the sets presented here is assessed to some extent, by using them to approximate integrals (over an octant of the unit sphere) of various high order spherical harmonics. When this is done, errors in the tabulated QRA sets present themselves at the highest tabulated orders, whilst combinations of the new QRS quadrature sets offer some improvements in accuracy over the original QRA sets. Finally, in order to offer a quick, visual understanding of the various quadrature sets presented, when combined to give product sets for the purposes of integrating functions confined to the surface of a sphere, three-dimensional representations of points located on an octant of the unit sphere (as in [8,12]) are shown.« less

  5. Improving the convergence rate in affine registration of PET and SPECT brain images using histogram equalization.

    PubMed

    Salas-Gonzalez, D; Górriz, J M; Ramírez, J; Padilla, P; Illán, I A

    2013-01-01

    A procedure to improve the convergence rate for affine registration methods of medical brain images when the images differ greatly from the template is presented. The methodology is based on a histogram matching of the source images with respect to the reference brain template before proceeding with the affine registration. The preprocessed source brain images are spatially normalized to a template using a general affine model with 12 parameters. A sum of squared differences between the source images and the template is considered as objective function, and a Gauss-Newton optimization algorithm is used to find the minimum of the cost function. Using histogram equalization as a preprocessing step improves the convergence rate in the affine registration algorithm of brain images as we show in this work using SPECT and PET brain images.

  6. Candidate genes for obesity-susceptibility show enriched association within a large genome-wide association study for BMI.

    PubMed

    Vimaleswaran, Karani S; Tachmazidou, Ioanna; Zhao, Jing Hua; Hirschhorn, Joel N; Dudbridge, Frank; Loos, Ruth J F

    2012-10-15

    Before the advent of genome-wide association studies (GWASs), hundreds of candidate genes for obesity-susceptibility had been identified through a variety of approaches. We examined whether those obesity candidate genes are enriched for associations with body mass index (BMI) compared with non-candidate genes by using data from a large-scale GWAS. A thorough literature search identified 547 candidate genes for obesity-susceptibility based on evidence from animal studies, Mendelian syndromes, linkage studies, genetic association studies and expression studies. Genomic regions were defined to include the genes ±10 kb of flanking sequence around candidate and non-candidate genes. We used summary statistics publicly available from the discovery stage of the genome-wide meta-analysis for BMI performed by the genetic investigation of anthropometric traits consortium in 123 564 individuals. Hypergeometric, rank tail-strength and gene-set enrichment analysis tests were used to test for the enrichment of association in candidate compared with non-candidate genes. The hypergeometric test of enrichment was not significant at the 5% P-value quantile (P = 0.35), but was nominally significant at the 25% quantile (P = 0.015). The rank tail-strength and gene-set enrichment tests were nominally significant for the full set of genes and borderline significant for the subset without SNPs at P < 10(-7). Taken together, the observed evidence for enrichment suggests that the candidate gene approach retains some value. However, the degree of enrichment is small despite the extensive number of candidate genes and the large sample size. Studies that focus on candidate genes have only slightly increased chances of detecting associations, and are likely to miss many true effects in non-candidate genes, at least for obesity-related traits.

  7. On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Fathizadeh, Farzad; Gabriel, Olivier

    2016-02-01

    The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge-de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

  8. Linking normative models of natural tasks to descriptive models of neural response.

    PubMed

    Jaini, Priyank; Burge, Johannes

    2017-10-01

    Understanding how nervous systems exploit task-relevant properties of sensory stimuli to perform natural tasks is fundamental to the study of perceptual systems. However, there are few formal methods for determining which stimulus properties are most useful for a given natural task. As a consequence, it is difficult to develop principled models for how to compute task-relevant latent variables from natural signals, and it is difficult to evaluate descriptive models fit to neural response. Accuracy maximization analysis (AMA) is a recently developed Bayesian method for finding the optimal task-specific filters (receptive fields). Here, we introduce AMA-Gauss, a new faster form of AMA that incorporates the assumption that the class-conditional filter responses are Gaussian distributed. Then, we use AMA-Gauss to show that its assumptions are justified for two fundamental visual tasks: retinal speed estimation and binocular disparity estimation. Next, we show that AMA-Gauss has striking formal similarities to popular quadratic models of neural response: the energy model and the generalized quadratic model (GQM). Together, these developments deepen our understanding of why the energy model of neural response have proven useful, improve our ability to evaluate results from subunit model fits to neural data, and should help accelerate psychophysics and neuroscience research with natural stimuli.

  9. Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

    NASA Technical Reports Server (NTRS)

    Helenbrook, B. T.; Atkins, H. L.

    2006-01-01

    We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

  10. Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Miskovic, Olivera; Olea, Rodrigo

    2011-03-15

    We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of a Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics. These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, wemore » derive a quantum statistical relation directly from the Euclidean action and not from the integration of the first law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists, in addition to the bulk action, of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian.« less

  11. The process of learning in neural net models with Poisson and Gauss connectivities.

    PubMed

    Sivridis, L; Kotini, A; Anninos, P

    2008-01-01

    In this study we examined the dynamic behavior of isolated and non-isolated neural networks with chemical markers that follow a Poisson or Gauss distribution of connectivity. The Poisson distribution shows higher activity in comparison to the Gauss distribution although the latter has more connections that obliterated due to randomness. We examined 57 hematoxylin and eosin stained sections from an equal number of autopsy specimens with a diagnosis of "cerebral matter within normal limits". Neural counting was carried out in 5 continuous optic fields, with the use of a simple optical microscope connected to a computer (software programmer Nikon Act-1 vers-2). The number of neurons that corresponded to a surface was equal to 0.15 mm(2). There was a gradual reduction in the number of neurons as age increased. A mean value of 45.8 neurons /0.15 mm(2) was observed within the age range 21-25, 33 neurons /0.15 mm(2) within the age range 41-45, 19.3 neurons /0.15 mm(2) within the age range 56-60 years. After the age of 60 it was observed that the number of neurons per unit area stopped decreasing. A correlation was observed between these experimental findings and the theoretical neural model developed by professor Anninos and his colleagues. Equivalence between the mean numbers of neurons of the above mentioned age groups and the highest possible number of synaptic connections per neuron (highest number of synaptic connections corresponded to the age group 21-25) was created. We then used both inhibitory and excitatory post-synaptic potentials and applied these values to the Poisson and Gauss distributions, whereas the neuron threshold was varied between 3 and 5. According to the obtained phase diagrams, the hysteresis loops decrease as age increases. These findings were significant as the hysteresis loops can be regarded as the basis for short-term memory.

  12. Dynamic PET simulator via tomographic emission projection for kinetic modeling and parametric image studies.

    PubMed

    Häggström, Ida; Beattie, Bradley J; Schmidtlein, C Ross

    2016-06-01

    To develop and evaluate a fast and simple tool called dpetstep (Dynamic PET Simulator of Tracers via Emission Projection), for dynamic PET simulations as an alternative to Monte Carlo (MC), useful for educational purposes and evaluation of the effects of the clinical environment, postprocessing choices, etc., on dynamic and parametric images. The tool was developed in matlab using both new and previously reported modules of petstep (PET Simulator of Tracers via Emission Projection). Time activity curves are generated for each voxel of the input parametric image, whereby effects of imaging system blurring, counting noise, scatters, randoms, and attenuation are simulated for each frame. Each frame is then reconstructed into images according to the user specified method, settings, and corrections. Reconstructed images were compared to MC data, and simple Gaussian noised time activity curves (GAUSS). dpetstep was 8000 times faster than MC. Dynamic images from dpetstep had a root mean square error that was within 4% on average of that of MC images, whereas the GAUSS images were within 11%. The average bias in dpetstep and MC images was the same, while GAUSS differed by 3% points. Noise profiles in dpetstep images conformed well to MC images, confirmed visually by scatter plot histograms, and statistically by tumor region of interest histogram comparisons that showed no significant differences (p < 0.01). Compared to GAUSS, dpetstep images and noise properties agreed better with MC. The authors have developed a fast and easy one-stop solution for simulations of dynamic PET and parametric images, and demonstrated that it generates both images and subsequent parametric images with very similar noise properties to those of MC images, in a fraction of the time. They believe dpetstep to be very useful for generating fast, simple, and realistic results, however since it uses simple scatter and random models it may not be suitable for studies investigating these phenomena. dpetstep can be downloaded free of cost from https://github.com/CRossSchmidtlein/dPETSTEP.

  13. Designing a two-rank acceptance sampling plan for quality inspection of geospatial data products

    NASA Astrophysics Data System (ADS)

    Tong, Xiaohua; Wang, Zhenhua; Xie, Huan; Liang, Dan; Jiang, Zuoqin; Li, Jinchao; Li, Jun

    2011-10-01

    To address the disadvantages of classical sampling plans designed for traditional industrial products, we originally propose a two-rank acceptance sampling plan (TRASP) for the inspection of geospatial data outputs based on the acceptance quality level (AQL). The first rank sampling plan is to inspect the lot consisting of map sheets, and the second is to inspect the lot consisting of features in an individual map sheet. The TRASP design is formulated as an optimization problem with respect to sample size and acceptance number, which covers two lot size cases. The first case is for a small lot size with nonconformities being modeled by a hypergeometric distribution function, and the second is for a larger lot size with nonconformities being modeled by a Poisson distribution function. The proposed TRASP is illustrated through two empirical case studies. Our analysis demonstrates that: (1) the proposed TRASP provides a general approach for quality inspection of geospatial data outputs consisting of non-uniform items and (2) the proposed acceptance sampling plan based on TRASP performs better than other classical sampling plans. It overcomes the drawbacks of percent sampling, i.e., "strictness for large lot size, toleration for small lot size," and those of a national standard used specifically for industrial outputs, i.e., "lots with different sizes corresponding to the same sampling plan."

  14. GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition

    NASA Astrophysics Data System (ADS)

    Zhen, Z.; Jia, X.

    2014-12-01

    Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the speedup ratio time consumption of RTM is 11.5. At the same time, the accuracy of imaging is not harmed. Another advantage of the GPUs-GPP method is its easy applications in other numerical methods such as the FEM. Finally, in the GPUs-GPP method, the arrays require quite limited memory storage, which makes the method promising in dealing with large-scale 3D problems.

  15. The mean magnetic field of the sun: Observations at Stanford

    NASA Technical Reports Server (NTRS)

    Scherrer, P. H.; Wilcox, J. M.; Svalgaard, L.; Duvall, T. L., Jr.; Dittmer, P. H.; Gustafson, E. K.

    1977-01-01

    A solar telescope was built at Stanford University to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph which is connected to a 22.9 m vertical Littrow spectrograph. Sun-as-a-star integrated light measurements of the mean solar magnetic field were made daily since May 1975. The typical mean field magnitude is about 0.15 gauss with typical measurement error less than 0.05 gauss. The mean field polarity pattern is essentially identical to the interplanetary magnetic field sector structure (seen near the earth with a 4 day lag). The differences in the observed structures can be understood in terms of a warped current sheet model.

  16. Analysis of radial and longitudinal field of plasma wakefield generated by a Laguerre-Gauss laser pulse

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Firouzjaei, Ali Shekari; Shokri, Babak

    In the present paper, we study the wakes known as the donut wake which is generated by Laguerre-Gauss (LG) laser pulses. Effects of the special spatial profile of a LG pulse on the radial and longitudinal wakefields are presented via an analytical model in a weakly non-linear regime in two dimensions. Different aspects of the donut-shaped wakefields have been analyzed and compared with Gaussian-driven wakes. There is also some discussion about the accelerating-focusing phase of the donut wake. Variations of longitudinal and radial wakes with laser amplitude, pulse length, and pulse spot size have been presented and discussed. Finally, wemore » present the optimum pulse duration for such wakes.« less

  17. Automatic Fourier transform and self-Fourier beams due to parabolic potential

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

    We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

  18. Coarse-to-fine markerless gait analysis based on PCA and Gauss-Laguerre decomposition

    NASA Astrophysics Data System (ADS)

    Goffredo, Michela; Schmid, Maurizio; Conforto, Silvia; Carli, Marco; Neri, Alessandro; D'Alessio, Tommaso

    2005-04-01

    Human movement analysis is generally performed through the utilization of marker-based systems, which allow reconstructing, with high levels of accuracy, the trajectories of markers allocated on specific points of the human body. Marker based systems, however, show some drawbacks that can be overcome by the use of video systems applying markerless techniques. In this paper, a specifically designed computer vision technique for the detection and tracking of relevant body points is presented. It is based on the Gauss-Laguerre Decomposition, and a Principal Component Analysis Technique (PCA) is used to circumscribe the region of interest. Results obtained on both synthetic and experimental tests provide significant reduction of the computational costs, with no significant reduction of the tracking accuracy.

  19. On optimal improvements of classical iterative schemes for Z-matrices

    NASA Astrophysics Data System (ADS)

    Noutsos, D.; Tzoumas, M.

    2006-04-01

    Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.

  20. Evolution of hydromagnetic turbulence from the electroweak phase transition

    NASA Astrophysics Data System (ADS)

    Brandenburg, Axel; Kahniashvili, Tina; Mandal, Sayan; Pol, Alberto Roper; Tevzadze, Alexander G.; Vachaspati, Tanmay

    2017-12-01

    We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early Universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early Universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today.

  1. Dilaton field released under collision of dilatonic black holes with Gauss-Bonnet term

    NASA Astrophysics Data System (ADS)

    Gwak, Bogeun; Ro, Daeho

    2017-08-01

    We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the dilaton hair is maximized when the horizon of one black hole is minimized for a fixed second black hole.

  2. 4d N = 1 quiver gauge theories and the An Bailey lemma

    NASA Astrophysics Data System (ADS)

    Brünner, Frederic; Spiridonov, Vyacheslav P.

    2018-03-01

    We study the integral Bailey lemma associated with the An-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional N = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

  3. Goodness-of-fit tests for open capture-recapture models

    USGS Publications Warehouse

    Pollock, K.H.; Hines, J.E.; Nichols, J.D.

    1985-01-01

    General goodness-of-fit tests for the Jolly-Seber model are proposed. These tests are based on conditional arguments using minimal sufficient statistics. The tests are shown to be of simple hypergeometric form so that a series of independent contingency table chi-square tests can be performed. The relationship of these tests to other proposed tests is discussed. This is followed by a simulation study of the power of the tests to detect departures from the assumptions of the Jolly-Seber model. Some meadow vole capture-recapture data are used to illustrate the testing procedure which has been implemented in a computer program available from the authors.

  4. Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

    PubMed

    Sasaki, Ryu

    2011-03-28

    A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

  5. Linking matrices in systems with periodic boundary conditions

    NASA Astrophysics Data System (ADS)

    Panagiotou, Eleni; Millett, Kenneth C.

    2018-06-01

    We study the linking matrix, a measure of entanglement for a collection of closed or open chains in 3-space based on the Gauss linking number. Periodic boundary conditions (PBC) are often used in the simulation of physical systems of filaments. To measure entanglement of closed or open chains in systems employing PBC we use the periodic linking matrix, based on the periodic linking number, defined in Panagiotou (2015 J. Comput. Phys. 300 533–73). We study the properties of the periodic linking matrix as a function of cell size. We provide analytical results concerning the eigenvalues of the periodic linking matrix and show that some of them are invariant of cell-size.

  6. Instability analysis of expansion-free sphere in f(𝒢) gravity

    NASA Astrophysics Data System (ADS)

    Sharif, M.; Ikram, Ayesha

    The aim of this paper is to study the dynamical instability of expansion-free spherically symmetric anisotropic fluid in the framework of f(𝒢) gravity. We apply perturbation scheme of the first-order to the metric functions as well as matter variables and construct modified field equations for both static and perturbed configurations using power-law f(𝒢) model. To discuss the instability dynamics, we use the contracted Bianchi identities to formulate the dynamical equations in both Newtonian and post-Newtonian regimes. It is found that the range of instability is independent of adiabatic index for expansion-free fluid but depends on anisotropic pressures, energy density and Gauss-Bonnet (GB) terms.

  7. Study of static wormhole solutions in F(T ,TG) gravity

    NASA Astrophysics Data System (ADS)

    Sharif, M.; Nazir, Kanwal

    2018-06-01

    In this paper, we investigate static spherically symmetric wormhole solutions in the background of F(T ,TG) gravity (T is the torsion scalar and TG represents teleparallel equivalent of the Gauss-Bonnet term). We study the wormhole solutions by assuming four different matter contents, a specific redshift function and a particular F(T ,TG) model. The behavior of null/weak energy conditions for these fluids is analyzed graphically. It turns out that wormhole solutions can be obtained in the absence of exotic matter for some particular regions of spacetime. We also explore stability of wormhole solutions through equilibrium condition. It is concluded that there exist physically acceptable wormhole solutions for anisotropic, isotropic and traceless fluids.

  8. Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement.

    PubMed

    Nguyen, N; Milanfar, P; Golub, G

    2001-01-01

    In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method.

  9. Gravitational Collapse of Magnetized Clouds. II. The Role of Ohmic Dissipation

    NASA Astrophysics Data System (ADS)

    Shu, Frank H.; Galli, Daniele; Lizano, Susana; Cai, Mike

    2006-08-01

    We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi-steady state and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and hypergeometric confluent functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by at least 1 order of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.

  10. GO-Bayes: Gene Ontology-based overrepresentation analysis using a Bayesian approach.

    PubMed

    Zhang, Song; Cao, Jing; Kong, Y Megan; Scheuermann, Richard H

    2010-04-01

    A typical approach for the interpretation of high-throughput experiments, such as gene expression microarrays, is to produce groups of genes based on certain criteria (e.g. genes that are differentially expressed). To gain more mechanistic insights into the underlying biology, overrepresentation analysis (ORA) is often conducted to investigate whether gene sets associated with particular biological functions, for example, as represented by Gene Ontology (GO) annotations, are statistically overrepresented in the identified gene groups. However, the standard ORA, which is based on the hypergeometric test, analyzes each GO term in isolation and does not take into account the dependence structure of the GO-term hierarchy. We have developed a Bayesian approach (GO-Bayes) to measure overrepresentation of GO terms that incorporates the GO dependence structure by taking into account evidence not only from individual GO terms, but also from their related terms (i.e. parents, children, siblings, etc.). The Bayesian framework borrows information across related GO terms to strengthen the detection of overrepresentation signals. As a result, this method tends to identify sets of closely related GO terms rather than individual isolated GO terms. The advantage of the GO-Bayes approach is demonstrated with a simulation study and an application example.

  11. 15-digit accuracy calculations of Chandrasekhar's H-function for isotropic scattering by means of the double exponential formula

    NASA Astrophysics Data System (ADS)

    Kawabata, Kiyoshi

    2016-12-01

    This work shows that it is possible to calculate numerical values of the Chandrasekhar H-function for isotropic scattering at least with 15-digit accuracy by making use of the double exponential formula (DE-formula) of Takahashi and Mori (Publ. RIMS, Kyoto Univ. 9:721, 1974) instead of the Gauss-Legendre quadrature employed in the numerical scheme of Kawabata and Limaye (Astrophys. Space Sci. 332:365, 2011) and simultaneously taking a precautionary measure to minimize the effects due to loss of significant digits particularly in the cases of near-conservative scattering and/or errors involved in returned values of library functions supplied by compilers in use. The results of our calculations are presented for 18 selected values of single scattering albedo π0 and 22 values of an angular variable μ, the cosine of zenith angle θ specifying the direction of radiation incident on or emergent from semi-infinite media.

  12. Generalized Israel junction conditions for a fourth-order brane world

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Balcerzak, Adam; Dabrowski, Mariusz P.

    2008-01-15

    We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to themore » field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.« less

  13. Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes

    NASA Astrophysics Data System (ADS)

    Calvo, M.; González-Pinto, S.; Montijano, J. I.

    2008-09-01

    Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance [delta], attempt to advance the integration selecting the size of each step so that some measure of the local error is [similar, equals][delta]. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188-200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109-123] and the extensions of Higham [Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227-236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge-Kutta codes the global errors behave asymptotically as some rational power of [delta]. This step-size policy, for a given IVP, determines at each grid point tn a new step-size hn+1=h(tn;[delta]) so that h(t;[delta]) is a continuous function of t. In this paper a study of the tolerance proportionality property under a discontinuous step-size policy that does not allow to change the size of the step if the step-size ratio between two consecutive steps is close to unity is carried out. This theory is applied to obtain global error estimations in a few problems that have been solved with the code Gauss2 [S. Gonzalez-Pinto, R. Rojas-Bello, Gauss2, a Fortran 90 code for second order initial value problems, ], based on an adaptive two stage Runge-Kutta-Gauss method with this discontinuous step-size policy.

  14. Image texture segmentation using a neural network

    NASA Astrophysics Data System (ADS)

    Sayeh, Mohammed R.; Athinarayanan, Ragu; Dhali, Pushpuak

    1992-09-01

    In this paper we use a neural network called the Lyapunov associative memory (LYAM) system to segment image texture into different categories or clusters. The LYAM system is constructed by a set of ordinary differential equations which are simulated on a digital computer. The clustering can be achieved by using a single tuning parameter in the simplest model. Pattern classes are represented by the stable equilibrium states of the system. Design of the system is based on synthesizing two local energy functions, namely, the learning and recall energy functions. Before the implementation of the segmentation process, a Gauss-Markov random field (GMRF) model is applied to the raw image. This application suitably reduces the image data and prepares the texture information for the neural network process. We give a simple image example illustrating the capability of the technique. The GMRF-generated features are also used for a clustering, based on the Euclidean distance.

  15. Mathematical model of optical signals emitted by electrical discharges occuring in electroinsulating oil

    NASA Astrophysics Data System (ADS)

    Kozioł, Michał

    2017-10-01

    The article presents a parametric model describing the registered distributions spectrum of optical radiation emitted by electrical discharges generated in the systems: the needle- needle, the needleplate and in the system for surface discharges. Generation of electrical discharges and registration of the emitted radiation was carried out in three different electrical insulating oils: fabric new, operated (used) and operated with air bubbles. For registration of optical spectra in the range of ultraviolet, visible and near infrared a high resolution spectrophotometer was. The proposed mathematical model was developed in a regression procedure using gauss-sigmoid type function. The dependent variable was the intensity of the recorded optical signals. In order to estimate the optimal parameters of the model an evolutionary algorithm was used. The optimization procedure was performed in Matlab environment. For determination of the matching quality of theoretical parameters of the regression function to the empirical data determination coefficient R2 was applied.

  16. Shape dependence of holographic Rényi entropy in general dimensions

    DOE PAGES

    Bianchi, Lorenzo; Chapman, Shira; Dong, Xi; ...

    2016-11-29

    We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove amore » set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.« less

  17. Mask patterning process using the negative tone chemically amplified resist TOK OEBR-CAN024

    NASA Astrophysics Data System (ADS)

    Irmscher, Mathias; Beyer, Dirk; Butschke, Joerg; Hudek, Peter; Koepernik, Corinna; Plumhoff, Jason; Rausa, Emmanuel; Sato, Mitsuru; Voehringer, Peter

    2004-08-01

    Optimized process parameters using the TOK OEBR-CAN024 resist for high chrome load patterning have been determined. A tight linearity tolerance for opaque and clear features, independent on the local pattern density, was the goal of our process integration work. For this purpose we evaluated a new correction method taking into account electron scattering and process influences. The method is based on matching of measured pattern geometry by iterative back-simulation using multiple Gauss and/or exponential functions. The obtained control function acts as input for the proximity correction software PROXECCO. Approaches with different pattern oversize and two Cr thicknesses were accomplished and the results have been reported. Isolated opaque and clear lines could be realized in a very tight linearity range. The increasing line width of small dense lines, induced by the etching process, could be corrected only partially.

  18. Quantitative three-dimensional ice roughness from scanning electron microscopy

    NASA Astrophysics Data System (ADS)

    Butterfield, Nicholas; Rowe, Penny M.; Stewart, Emily; Roesel, David; Neshyba, Steven

    2017-03-01

    We present a method for inferring surface morphology of ice from scanning electron microscope images. We first develop a novel functional form for the backscattered electron intensity as a function of ice facet orientation; this form is parameterized using smooth ice facets of known orientation. Three-dimensional representations of rough surfaces are retrieved at approximately micrometer resolution using Gauss-Newton inversion within a Bayesian framework. Statistical analysis of the resulting data sets permits characterization of ice surface roughness with a much higher statistical confidence than previously possible. A survey of results in the range -39°C to -29°C shows that characteristics of the roughness (e.g., Weibull parameters) are sensitive not only to the degree of roughening but also to the symmetry of the roughening. These results suggest that roughening characteristics obtained by remote sensing and in situ measurements of atmospheric ice clouds can potentially provide more facet-specific information than has previously been appreciated.

  19. On a quadrature formula of Gori and Micchelli

    NASA Astrophysics Data System (ADS)

    Yang, Shijun

    2005-04-01

    Sparked by Bojanov (J. Comput. Appl. Math. 70 (1996) 349), we provide an alternate approach to quadrature formulas based on the zeros of the Chebyshev polynomial of the first kind for any weight function w introduced and studied in Gori and Micchelli (Math. Comp. 65 (1996) 1567), thereby improving on their observations. Upon expansion of the divided differences, we obtain explicit expressions for the corresponding Cotes coefficients in Gauss-Turan quadrature formulas for and I(fTn;w) for a Gori-Micchelli weight function. It is also interesting to mention what has been neglected for about 30 years by the literature is that, as a consequence of expansion of the divided differences in the special case when , the solution of the famous Turan's Problem 26 raised in 1980 was in fact implied by a result of Micchelli and Rivlin (IBM J. Res. Develop. 16 (1972) 372) in 1972. Some concluding comments are made in the final section.

  20. Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

    NASA Astrophysics Data System (ADS)

    Auteri, F.; Quartapelle, L.; Vigevano, L.

    2002-08-01

    This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

  1. Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

    NASA Astrophysics Data System (ADS)

    Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

    2017-08-01

    Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

  2. Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels.

    PubMed

    Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

    2017-08-01

    Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

  3. An accurate and efficient method for piezoelectric coated functional devices based on the two-dimensional Green’s function for a normal line force and line charge

    NASA Astrophysics Data System (ADS)

    Hou, Peng-Fei; Zhang, Yang

    2017-09-01

    Because most piezoelectric functional devices, including sensors, actuators and energy harvesters, are in the form of a piezoelectric coated structure, it is valuable to present an accurate and efficient method for obtaining the electro-mechanical coupling fields of this coated structure under mechanical and electrical loads. With this aim, the two-dimensional Green’s function for a normal line force and line charge on the surface of coated structure, which is a combination of an orthotropic piezoelectric coating and orthotropic elastic substrate, is presented in the form of elementary functions based on the general solution method. The corresponding electro-mechanical coupling fields of this coated structure under arbitrary mechanical and electrical loads can then be obtained by the superposition principle and Gauss integration. Numerical results show that the presented method has high computational precision, efficiency and stability. It can be used to design the best coating thickness in functional devices, improve the sensitivity of sensors, and improve the efficiency of actuators and energy harvesters. This method could be an efficient tool for engineers in engineering applications.

  4. The Green’s functions for peridynamic non-local diffusion

    PubMed Central

    Wang, L. J.; Xu, J. F.

    2016-01-01

    In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

  5. Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

    PubMed

    Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

    2003-11-01

    A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

  6. Minimax confidence intervals in geomagnetism

    NASA Technical Reports Server (NTRS)

    Stark, Philip B.

    1992-01-01

    The present paper uses theory of Donoho (1989) to find lower bounds on the lengths of optimally short fixed-length confidence intervals (minimax confidence intervals) for Gauss coefficients of the field of degree 1-12 using the heat flow constraint. The bounds on optimal minimax intervals are about 40 percent shorter than Backus' intervals: no procedure for producing fixed-length confidence intervals, linear or nonlinear, can give intervals shorter than about 60 percent the length of Backus' in this problem. While both methods rigorously account for the fact that core field models are infinite-dimensional, the application of the techniques to the geomagnetic problem involves approximations and counterfactual assumptions about the data errors, and so these results are likely to be extremely optimistic estimates of the actual uncertainty in Gauss coefficients.

  7. Constraining some Horndeski gravity theories

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Sourav; Chakraborty, Sumanta

    2017-02-01

    We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar-tensor) theory in the context of Solar System and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in Maeda and Dadhich [Phys. Rev. D 75, 044007 (2007), 10.1103/PhysRevD.75.044007] and Sotiriou and Zhou [Phys. Rev. D 90, 124063 (2014), 10.1103/PhysRevD.90.124063], respectively. The latter, in particular, applies only to black-hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

  8. Flare research with the NASA/MSFC vector magnetograph - Observed characteristics of sheared magnetic fields that produce flares

    NASA Technical Reports Server (NTRS)

    Moore, R. L.; Hagyard, M. J.; Davis, J. M.

    1987-01-01

    The present MSFC Vector Magnetograph has sufficient spatial resolution (2.7 arcsec pixels) and sensitivity to the transverse field (the noise level is about 100 gauss) to map the transverse field in active regions accurately enough to reveal key aspects of the sheared magnetic fields commonly found at flare sites. From the measured shear angle along the polarity inversion line in sites that flared and in other shear sites that didn't flare, evidence is found that a sufficient condition for a flare to occur in 1000 gauss fields in and near sunspots is that both: (1) the maximum shear angle exceed 85 degrees; and (2) the extent of strong shear (shear angle of greater than 80 degrees) exceed 10,000 km.

  9. Asteroseismology can reveal strong internal magnetic fields in red giant stars.

    PubMed

    Fuller, Jim; Cantiello, Matteo; Stello, Dennis; Garcia, Rafael A; Bildsten, Lars

    2015-10-23

    Internal stellar magnetic fields are inaccessible to direct observations, and little is known about their amplitude, geometry, and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, arising from a magnetic greenhouse effect that scatters and traps oscillation-mode energy within the core of the star. The Kepler satellite has observed a few dozen red giants with depressed dipole modes, which we interpret as stars with strongly magnetized cores. We find that field strengths larger than ~10(5) gauss may produce the observed depression, and in one case we infer a minimum core field strength of ≈10(7) gauss. Copyright © 2015, American Association for the Advancement of Science.

  10. Nonparaxial fractional Bessel and Bessel-Gauss auto-focusing light-sheet pincers and their higher-order spatial derivatives

    NASA Astrophysics Data System (ADS)

    Mitri, F. G.

    2017-05-01

    Nonparaxial fractional electromagnetic Bessel and Bessel-Gauss auto-focusing light-sheet solutions and their spatial derivatives are synthesized stemming from the angular spectrum decomposition in plane waves. The propagation characteristics of these transverse electric-polarized light-sheets are analyzed by computing the radiated component of the incident electric field. Tight bending of the beam along curved trajectories and slit openings are observed, which could offer unique features and potential applications in the development of improved methods and devices in light-sheet tweezers for particle manipulation applications and dynamics in opto-fluidics, particle sizing and imaging to name a few examples. Moreover, computations of the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solutions.

  11. The Bassi Rebay 1 scheme is a special case of the Symmetric Interior Penalty formulation for discontinuous Galerkin discretisations with Gauss-Lobatto points

    NASA Astrophysics Data System (ADS)

    Manzanero, Juan; Rueda-Ramírez, Andrés M.; Rubio, Gonzalo; Ferrer, Esteban

    2018-06-01

    In the discontinuous Galerkin (DG) community, several formulations have been proposed to solve PDEs involving second-order spatial derivatives (e.g. elliptic problems). In this paper, we show that, when the discretisation is restricted to the usage of Gauss-Lobatto points, there are important similarities between two common choices: the Bassi-Rebay 1 (BR1) method, and the Symmetric Interior Penalty (SIP) formulation. This equivalence enables the extrapolation of properties from one scheme to the other: a sharper estimation of the minimum penalty parameter for the SIP stability (compared to the more general estimate proposed by Shahbazi [1]), more efficient implementations of the BR1 scheme, and the compactness of the BR1 method for straight quadrilateral and hexahedral meshes.

  12. A computational approach for hypersonic nonequilibrium radiation utilizing space partition algorithm and Gauss quadrature

    NASA Astrophysics Data System (ADS)

    Shang, J. S.; Andrienko, D. A.; Huang, P. G.; Surzhikov, S. T.

    2014-06-01

    An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical-physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss-Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.

  13. A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

    2014-02-01

    This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

  14. Characterization of near-stoichiometric Ti:LiNbO(3) strip waveguides with varied substrate refractive index in the guiding layer.

    PubMed

    Zhang, De-Long; Zhang, Pei; Zhou, Hao-Jiang; Pun, Edwin Yue-Bun

    2008-10-01

    We have demonstrated the possibility that near-stoichiometric Ti:LiNbO(3) strip waveguides are fabricated by carrying out vapor transport equilibration at 1060 degrees C for 12 h on a congruent LiNbO(3) substrate with photolithographically patterned 4-8 microm wide, 115 nm thick Ti strips. Optical characterizations show that these waveguides are single mode at 1.5 microm and show a waveguide loss of 1.3 dB/cm for TM mode and 1.1 dB/cm for TE mode. In the width/depth direction of the waveguide, the mode field follows the Gauss/Hermite-Gauss function. Secondary-ion-mass spectrometry (SIMS) was used to study Ti-concentration profiles in the depth direction and on the surface of the 6 microm wide waveguide. The result shows that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. The surface Ti concentration, 1/e width and depth, and mean diffusivities along the width and depth directions of the guide are similar to 3.0 x 10(21) cm(-3), 3.8 microm, 2.6 microm, 0.30 and 0.14 microm(2)/h, respectively. Micro-Raman analysis was carried out on the waveguide endface to characterize the depth profile of Li composition in the guiding layer. The results show that the depth profile of Li composition also follows a complementary error function with a 1/e depth of 3.64 microm. The mean ([Li(Li)]+[Ti(Li)])/([Nb(Nb)]+[Ti(Nb)]) ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer. A two-dimensional refractive index profile model in the waveguide is proposed by taking into consideration the varied substrate index and assuming linearity between Ti-induced index change and Ti concentration. The net waveguide surface index increments at 1545 nm are 0.0114 and 0.0212 for ordinary and extraordinary rays, respectively. Based upon the constructed index model, the fundamental mode field profile was calculated using the beam propagation method, and the mode sizes and effective index versus the Ti-strip width were calculated for three lower TM and TE modes using the variational method. An agreement between theory and experiment is obtained.

  15. Challenges in designing appropriate scaffolding to improve students' representational consistency: The case of a Gauss's law problem

    NASA Astrophysics Data System (ADS)

    Maries, Alexandru; Lin, Shih-Yin; Singh, Chandralekha

    2017-12-01

    Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students' representational consistency. Students in calculus-based introductory physics were given a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution in which they were asked to write a mathematical expression for the electric field in various regions and then plot the electric field. In study 1, we found that students had great difficulty in plotting the electric field as a function of the distance from the center of the sphere consistent with the mathematical expressions in various regions, and interviews with students suggested possible reasons which may account for this difficulty. Therefore, in study 2, we designed two scaffolding interventions with levels of support which built on each other (i.e., the second scaffolding level built on the first) in order to help students plot their expressions consistently and compared the performance of students provided with scaffolding with a comparison group which was not given any scaffolding support. Analysis of student performance with different levels of scaffolding reveals that scaffolding from an expert perspective beyond a certain level may sometimes hinder student performance and students may not even discern the relevance of the additional support. We provide possible interpretations for these findings based on in-depth, think-aloud student interviews.

  16. A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

    PubMed

    Mang, Andreas; Ruthotto, Lars

    2017-01-01

    We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

  17. The importance of excluded solvent volume effects in computing hydration free energies.

    PubMed

    Yang, Pei-Kun; Lim, Carmay

    2008-11-27

    Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.

  18. Dynamic PET simulator via tomographic emission projection for kinetic modeling and parametric image studies

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Häggström, Ida, E-mail: haeggsti@mskcc.org; Beattie, Bradley J.; Schmidtlein, C. Ross

    2016-06-15

    Purpose: To develop and evaluate a fast and simple tool called dPETSTEP (Dynamic PET Simulator of Tracers via Emission Projection), for dynamic PET simulations as an alternative to Monte Carlo (MC), useful for educational purposes and evaluation of the effects of the clinical environment, postprocessing choices, etc., on dynamic and parametric images. Methods: The tool was developed in MATLAB using both new and previously reported modules of PETSTEP (PET Simulator of Tracers via Emission Projection). Time activity curves are generated for each voxel of the input parametric image, whereby effects of imaging system blurring, counting noise, scatters, randoms, and attenuationmore » are simulated for each frame. Each frame is then reconstructed into images according to the user specified method, settings, and corrections. Reconstructed images were compared to MC data, and simple Gaussian noised time activity curves (GAUSS). Results: dPETSTEP was 8000 times faster than MC. Dynamic images from dPETSTEP had a root mean square error that was within 4% on average of that of MC images, whereas the GAUSS images were within 11%. The average bias in dPETSTEP and MC images was the same, while GAUSS differed by 3% points. Noise profiles in dPETSTEP images conformed well to MC images, confirmed visually by scatter plot histograms, and statistically by tumor region of interest histogram comparisons that showed no significant differences (p < 0.01). Compared to GAUSS, dPETSTEP images and noise properties agreed better with MC. Conclusions: The authors have developed a fast and easy one-stop solution for simulations of dynamic PET and parametric images, and demonstrated that it generates both images and subsequent parametric images with very similar noise properties to those of MC images, in a fraction of the time. They believe dPETSTEP to be very useful for generating fast, simple, and realistic results, however since it uses simple scatter and random models it may not be suitable for studies investigating these phenomena. dPETSTEP can be downloaded free of cost from https://github.com/CRossSchmidtlein/dPETSTEP.« less

  19. Hollow sinh-Gaussian beams and their paraxial properties.

    PubMed

    Sun, Qiongge; Zhou, Keya; Fang, Guangyu; Zhang, Guoqiang; Liu, Zhengjun; Liu, Shutian

    2012-04-23

    A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically. © 2012 Optical Society of America

  20. Superbounce and loop quantum ekpyrotic cosmologies from modified gravity: F(R) , F(G) and F(T) theories

    NASA Astrophysics Data System (ADS)

    Odintsov, S. D.; Oikonomou, V. K.; Saridakis, Emmanuel N.

    2015-12-01

    We investigate the realization of two bouncing paradigms, namely of the superbounce and the loop quantum cosmological ekpyrosis, in the framework of various modified gravities. In particular, we focus on the F(R) , F(G) and F(T) gravities, and we reconstruct their specific subclasses which lead to such universe evolutions. These subclasses constitute from power laws, polynomials, or hypergeometric ansatzes, which can be approximated by power laws. The qualitative similarity of the different effective gravities which realize the above two bouncing cosmologies, indicates that a universality might be lying behind the bounce. Finally, performing a linear perturbation analysis, we show that the obtained solutions are conditionally or fully stable.

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